Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

why i take intgral from equation it must apply for each term but just by sign is show up how it will work?

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(w(x, t))

w(x, t)*`will now be displayed as`*w

(2)

declare(f(x, t))

f(x, t)*`will now be displayed as`*f

(3)

NULL

pde := diff(w(x, t), `$`(t, 2))-a*(diff(w(x, t), `$`(x, 4)))-b*(diff(w(x, t), `$`(x, 2), `$`(t, 2)))+(diff(w(x, t), t))*(diff(w(x, t), `$`(x, 2)))+2*(diff(w(x, t), x))*(diff(w(x, t), x, t)) = 0

diff(diff(w(x, t), t), t)-a*(diff(diff(diff(diff(w(x, t), x), x), x), x))-b*(diff(diff(diff(diff(w(x, t), t), t), x), x))+(diff(w(x, t), t))*(diff(diff(w(x, t), x), x))+2*(diff(w(x, t), x))*(diff(diff(w(x, t), t), x)) = 0

(4)

Y := w(x, t) = 2*(diff(ln(f(x, t)), `$`(x, 2)))

w(x, t) = 2*(diff(diff(f(x, t), x), x))/f(x, t)-2*(diff(f(x, t), x))^2/f(x, t)^2

(5)

L := eval(pde, Y)

2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))/f(x, t)^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-4*(diff(diff(f(x, t), t), x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-a*(2*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))/f(x, t)-12*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+60*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-30*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))^3/f(x, t)^4+240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))*(diff(diff(f(x, t), x), x))/f(x, t)^3-20*(diff(diff(diff(f(x, t), x), x), x))^2/f(x, t)^2+720*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4/f(x, t)^5-540*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2/f(x, t)^4+60*(diff(diff(f(x, t), x), x))^3/f(x, t)^3-240*(diff(f(x, t), x))^6/f(x, t)^6)-b*(32*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2/f(x, t)^3+16*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+12*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-48*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^4-240*(diff(f(x, t), x))^4*(diff(f(x, t), t))^2/f(x, t)^6+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+48*(diff(f(x, t), x))^4*(diff(diff(f(x, t), t), t))/f(x, t)^5-144*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))^2/f(x, t)^4+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-36*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), t))^2/f(x, t)^4-288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2/f(x, t)^4-144*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2/f(x, t)^4+288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))^2/f(x, t)^5+2*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))/f(x, t)+24*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)^3-8*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2-12*(diff(diff(diff(diff(f(x, t), t), t), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-4*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*(diff(f(x, t), t))/f(x, t)^2-16*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2-12*(diff(diff(diff(f(x, t), t), x), x))^2/f(x, t)^2+4*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2)+(2*(diff(diff(diff(f(x, t), t), x), x))/f(x, t)-2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))/f(x, t)^2-4*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(f(x, t), x))^2*(diff(f(x, t), t))/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), x), x), x), x))/f(x, t)-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+24*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-6*(diff(diff(f(x, t), x), x))^2/f(x, t)^2-12*(diff(f(x, t), x))^4/f(x, t)^4)+2*(2*(diff(diff(diff(f(x, t), x), x), x))/f(x, t)-6*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))/f(x, t)^2+4*(diff(f(x, t), x))^3/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), t), x), x), x))/f(x, t)-6*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))/f(x, t)^2-2*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))/f(x, t)^2+12*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3-6*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+12*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))/f(x, t)^3-12*(diff(f(x, t), x))^3*(diff(f(x, t), t))/f(x, t)^4) = 0

(6)

numer(lhs(2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))/f(x, t)^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-4*(diff(diff(f(x, t), t), x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-a*(2*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))/f(x, t)-12*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+60*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-30*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))^3/f(x, t)^4+240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))*(diff(diff(f(x, t), x), x))/f(x, t)^3-20*(diff(diff(diff(f(x, t), x), x), x))^2/f(x, t)^2+720*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4/f(x, t)^5-540*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2/f(x, t)^4+60*(diff(diff(f(x, t), x), x))^3/f(x, t)^3-240*(diff(f(x, t), x))^6/f(x, t)^6)-b*(32*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^3+16*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2/f(x, t)^4-144*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2/f(x, t)^4+288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))^2/f(x, t)^5+48*(diff(f(x, t), x))^4*(diff(diff(f(x, t), t), t))/f(x, t)^5-144*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))^2/f(x, t)^4-36*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+24*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)^3-8*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2-12*(diff(diff(diff(diff(f(x, t), t), t), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-4*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*(diff(f(x, t), t))/f(x, t)^2-16*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2+48*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2/f(x, t)^3+12*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-48*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^4-240*(diff(f(x, t), x))^4*(diff(f(x, t), t))^2/f(x, t)^6-288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^4+2*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))/f(x, t)-12*(diff(diff(diff(f(x, t), t), x), x))^2/f(x, t)^2)+(2*(diff(diff(diff(f(x, t), t), x), x))/f(x, t)-2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))/f(x, t)^2-4*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(f(x, t), x))^2*(diff(f(x, t), t))/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), x), x), x), x))/f(x, t)-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+24*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-6*(diff(diff(f(x, t), x), x))^2/f(x, t)^2-12*(diff(f(x, t), x))^4/f(x, t)^4)+2*(2*(diff(diff(diff(f(x, t), x), x), x))/f(x, t)-6*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))/f(x, t)^2+4*(diff(f(x, t), x))^3/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), t), x), x), x))/f(x, t)-6*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))/f(x, t)^2-2*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))/f(x, t)^2+12*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3-6*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+12*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))/f(x, t)^3-12*(diff(f(x, t), x))^3*(diff(f(x, t), t))/f(x, t)^4) = 0))*denom(rhs(2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))/f(x, t)^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-4*(diff(diff(f(x, t), t), x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-a*(2*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))/f(x, t)-12*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+60*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-30*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))^3/f(x, t)^4+240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))*(diff(diff(f(x, t), x), x))/f(x, t)^3-20*(diff(diff(diff(f(x, t), x), x), x))^2/f(x, t)^2+720*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4/f(x, t)^5-540*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2/f(x, t)^4+60*(diff(diff(f(x, t), x), x))^3/f(x, t)^3-240*(diff(f(x, t), x))^6/f(x, t)^6)-b*(32*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^3+16*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2/f(x, t)^4-144*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2/f(x, t)^4+288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))^2/f(x, t)^5+48*(diff(f(x, t), x))^4*(diff(diff(f(x, t), t), t))/f(x, t)^5-144*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))^2/f(x, t)^4-36*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+24*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)^3-8*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2-12*(diff(diff(diff(diff(f(x, t), t), t), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-4*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*(diff(f(x, t), t))/f(x, t)^2-16*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, 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x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-a*(2*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))/f(x, t)-12*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+60*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-30*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))^3/f(x, t)^4+240*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))*(diff(diff(f(x, t), x), x))/f(x, t)^3-20*(diff(diff(diff(f(x, t), x), x), x))^2/f(x, t)^2+720*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4/f(x, t)^5-540*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2/f(x, t)^4+60*(diff(diff(f(x, t), x), x))^3/f(x, t)^3-240*(diff(f(x, t), x))^6/f(x, t)^6)-b*(32*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^3+16*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2/f(x, t)^4-144*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2/f(x, t)^4+288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))^2/f(x, t)^5+48*(diff(f(x, t), x))^4*(diff(diff(f(x, t), t), t))/f(x, t)^5-144*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))^2/f(x, t)^4-36*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+24*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)^3-8*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2-12*(diff(diff(diff(diff(f(x, t), t), t), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-4*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*(diff(f(x, t), t))/f(x, t)^2-16*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2+48*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2/f(x, 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x))*(diff(f(x, t), x))/f(x, t)^2+4*(diff(f(x, t), x))^3/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), t), x), x), x))/f(x, t)-6*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))/f(x, t)^2-2*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))/f(x, t)^2+12*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3-6*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+12*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))/f(x, t)^3-12*(diff(f(x, t), x))^3*(diff(f(x, t), t))/f(x, t)^4) = 0))*denom(lhs(2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))/f(x, t)^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-4*(diff(diff(f(x, t), t), x))^2/f(x, t)^2+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))/f(x, t)^3-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2-12*(diff(f(x, t), 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x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(f(x, t), x), x))*(diff(diff(diff(f(x, t), t), t), x))*(diff(f(x, t), x))/f(x, t)^3+384*(diff(f(x, t), x))^3*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))/f(x, t)^5+32*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3+96*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))/f(x, t)^3+48*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))/f(x, t)^3-48*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))/f(x, t)^4-72*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2/f(x, t)^4-144*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2/f(x, t)^4+288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*(diff(f(x, t), x))^2/f(x, t)^5+48*(diff(f(x, t), x))^4*(diff(diff(f(x, t), t), t))/f(x, t)^5-144*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))^2/f(x, t)^4-36*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), t))^2/f(x, t)^4+24*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))/f(x, t)^3-8*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2-12*(diff(diff(diff(diff(f(x, t), t), t), x), x))*(diff(diff(f(x, t), x), x))/f(x, t)^2-4*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*(diff(f(x, t), t))/f(x, t)^2-16*(diff(diff(diff(diff(f(x, t), t), x), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(f(x, t), t))^2/f(x, t)^3-2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*(diff(diff(f(x, t), t), t))/f(x, t)^2-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^2+48*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2/f(x, t)^3+12*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))/f(x, t)^3-48*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))/f(x, t)^4-240*(diff(f(x, t), x))^4*(diff(f(x, t), t))^2/f(x, t)^6-288*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^4+2*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))/f(x, t)-12*(diff(diff(diff(f(x, t), t), x), x))^2/f(x, t)^2)+(2*(diff(diff(diff(f(x, t), t), x), x))/f(x, t)-2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))/f(x, t)^2-4*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+4*(diff(f(x, t), x))^2*(diff(f(x, t), t))/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), x), x), x), x))/f(x, t)-8*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), x))/f(x, t)^2+24*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2/f(x, t)^3-6*(diff(diff(f(x, t), x), x))^2/f(x, t)^2-12*(diff(f(x, t), x))^4/f(x, t)^4)+2*(2*(diff(diff(diff(f(x, t), x), x), x))/f(x, t)-6*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))/f(x, t)^2+4*(diff(f(x, t), x))^3/f(x, t)^3)*(2*(diff(diff(diff(diff(f(x, t), t), x), x), x))/f(x, t)-6*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))/f(x, t)^2-2*(diff(diff(diff(f(x, t), x), x), x))*(diff(f(x, t), t))/f(x, t)^2+12*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))/f(x, t)^3-6*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))/f(x, t)^2+12*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), x))/f(x, t)^3-12*(diff(f(x, t), x))^3*(diff(f(x, t), t))/f(x, t)^4) = 0))

2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*f(x, t)^6-4*(diff(diff(f(x, t), t), x))^2*f(x, t)^5-144*(diff(f(x, t), t))*(diff(f(x, t), x))^6-8*f(x, t)^4*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+120*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2+8*f(x, t)^3*(diff(f(x, t), t))*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))+96*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))+80*f(x, t)^3*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^2*(diff(diff(diff(f(x, t), x), x), x))-216*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2-96*f(x, t)^2*(diff(f(x, t), t))*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))-288*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3+360*f(x, t)*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)^3*(diff(diff(f(x, t), t), x))^2*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))*b+240*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))*a-720*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4*a-48*f(x, t)^2*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^4*b+240*f(x, t)*(diff(f(x, t), t))^2*(diff(f(x, t), x))^4*b-40*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-4*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))*f(x, t)^4-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))+36*f(x, t)^3*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))^2*b+540*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2*a-60*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a-24*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+8*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*b+8*f(x, t)^5*(diff(diff(diff(f(x, t), t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-4*f(x, t)^4*(diff(f(x, t), t))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b-12*f(x, t)^4*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2*b+12*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+2*f(x, t)^5*(diff(diff(f(x, t), t), t))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b+16*f(x, t)^5*(diff(diff(f(x, t), t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b+12*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*a+4*f(x, t)^5*(diff(f(x, t), t))*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*b+30*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a+144*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), t))^2*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b+72*f(x, t)^3*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2*b-288*f(x, t)^2*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2*b-384*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3*b+88*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-48*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*b-96*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*b-240*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*a-16*f(x, t)^4*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))*a-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))*b+12*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))^2*b+20*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))^2*a-60*f(x, t)^4*(diff(diff(f(x, t), x), x))^3*a+240*f(x, t)*(diff(f(x, t), x))^6*a-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*f(x, t)^5+4*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*f(x, t)^5-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*f(x, t)^5+8*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))-12*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*f(x, t)^4-8*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(diff(f(x, t), x), x), x))^2+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))*f(x, t)^4-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2*f(x, t)^3+12*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^3+16*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(diff(f(x, t), t), x), x), x))-72*f(x, t)^2*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^5+288*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b = 0

(7)

map(int, -8*f(x, t)^4*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+120*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2+8*f(x, t)^3*(diff(f(x, t), t))*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))+96*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))+80*f(x, t)^3*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^2*(diff(diff(diff(f(x, t), x), x), x))-216*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2-96*f(x, t)^2*(diff(f(x, t), t))*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))-288*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3+360*f(x, t)*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)^3*(diff(diff(f(x, t), t), x))^2*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))*b+240*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))*a-720*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4*a-48*f(x, t)^2*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^4*b+240*f(x, t)*(diff(f(x, t), t))^2*(diff(f(x, t), x))^4*b-40*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-4*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))*f(x, t)^4-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))+36*f(x, t)^3*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))^2*b+540*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2*a-60*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a-24*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+8*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*b+8*f(x, t)^5*(diff(diff(diff(f(x, t), t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-4*f(x, t)^4*(diff(f(x, t), t))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b-12*f(x, t)^4*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2*b+12*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+2*f(x, t)^5*(diff(diff(f(x, t), t), t))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b+16*f(x, t)^5*(diff(diff(f(x, t), t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b+12*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*a+4*f(x, t)^5*(diff(f(x, t), t))*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*b+30*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a+144*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), t))^2*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b+72*f(x, t)^3*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2*b-288*f(x, t)^2*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2*b-384*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3*b+88*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-48*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*b-96*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*b-240*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*a-16*f(x, t)^4*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b+2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*f(x, t)^6-4*(diff(diff(f(x, t), t), x))^2*f(x, t)^5-144*(diff(f(x, t), t))*(diff(f(x, t), x))^6-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))*a-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))*b+12*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))^2*b+20*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))^2*a-60*f(x, t)^4*(diff(diff(f(x, t), x), x))^3*a+240*f(x, t)*(diff(f(x, t), x))^6*a-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*f(x, t)^5+4*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*f(x, t)^5-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*f(x, t)^5+8*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))-12*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*f(x, t)^4-8*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(diff(f(x, t), x), x), x))^2+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))*f(x, t)^4-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2*f(x, t)^3+12*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^3+16*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(diff(f(x, t), t), x), x), x))-72*f(x, t)^2*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^5+288*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b = 0, x)

int(2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*f(x, t)^6-4*(diff(diff(f(x, t), t), x))^2*f(x, t)^5-144*(diff(f(x, t), t))*(diff(f(x, t), x))^6-8*f(x, t)^4*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+120*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2+8*f(x, t)^3*(diff(f(x, t), t))*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))+96*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))+80*f(x, t)^3*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^2*(diff(diff(diff(f(x, t), x), x), x))-216*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2-96*f(x, t)^2*(diff(f(x, t), t))*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))-288*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3+360*f(x, t)*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)^3*(diff(diff(f(x, t), t), x))^2*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), t), t), x))*b+240*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(f(x, t), x), x), x))*a-720*f(x, t)^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^4*a-48*f(x, t)^2*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^4*b+240*f(x, t)*(diff(f(x, t), t))^2*(diff(f(x, t), x))^4*b-40*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-4*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))+16*(diff(f(x, t), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), t))*f(x, t)^4-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))-24*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))+36*f(x, t)^3*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))^2*b+540*f(x, t)^3*(diff(diff(f(x, t), x), x))^2*(diff(f(x, t), x))^2*a-60*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a-24*f(x, t)^4*(diff(f(x, t), x))^2*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+8*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x))*b+8*f(x, t)^5*(diff(diff(diff(f(x, t), t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-4*f(x, t)^4*(diff(f(x, t), t))^2*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b-12*f(x, t)^4*(diff(diff(f(x, t), x), x))^2*(diff(diff(f(x, t), t), t))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))^2*b+12*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), t), t), x), x))*b+2*f(x, t)^5*(diff(diff(f(x, t), t), t))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*b+16*f(x, t)^5*(diff(diff(f(x, t), t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b+12*f(x, t)^5*(diff(f(x, t), x))*(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x))*a+4*f(x, t)^5*(diff(f(x, t), t))*(diff(diff(diff(diff(diff(f(x, t), t), x), x), x), x))*b+30*f(x, t)^5*(diff(diff(f(x, t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))*a+144*f(x, t)^3*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(f(x, t), x))^2*b+48*f(x, t)^3*(diff(f(x, t), t))^2*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b+72*f(x, t)^3*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))^2*b-288*f(x, t)^2*(diff(f(x, t), t))^2*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))^2*b-384*f(x, t)^2*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^3*b+88*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))-48*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*b-96*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(f(x, t), t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-32*f(x, t)^4*(diff(f(x, t), t))*(diff(f(x, t), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))*b-48*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*b-240*f(x, t)^4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*a-16*f(x, t)^4*(diff(diff(f(x, t), t), t))*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), x), x), x))*b-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), x), x), x), x), x), x))*a-2*f(x, t)^6*(diff(diff(diff(diff(diff(diff(f(x, t), t), t), x), x), x), x))*b+12*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))^2*b+20*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))^2*a-60*f(x, t)^4*(diff(diff(f(x, t), x), x))^3*a+240*f(x, t)*(diff(f(x, t), x))^6*a-4*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), t))*f(x, t)^5+4*f(x, t)^5*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(diff(diff(f(x, t), x), x), x), x))-2*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), t))*f(x, t)^5-4*(diff(f(x, t), x))*(diff(diff(diff(f(x, t), t), t), x))*f(x, t)^5+8*f(x, t)^5*(diff(diff(diff(f(x, t), x), x), x))*(diff(diff(diff(diff(f(x, t), t), x), x), x))-12*f(x, t)^4*(diff(diff(diff(f(x, t), t), x), x))*(diff(diff(f(x, t), x), x))^2+4*(diff(diff(f(x, t), x), x))*(diff(f(x, t), t))^2*f(x, t)^4-8*f(x, t)^4*(diff(f(x, t), t))*(diff(diff(diff(f(x, t), x), x), x))^2+4*(diff(f(x, t), x))^2*(diff(diff(f(x, t), t), t))*f(x, t)^4-12*(diff(f(x, t), x))^2*(diff(f(x, t), t))^2*f(x, t)^3+12*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))^3+16*f(x, t)^3*(diff(f(x, t), x))^3*(diff(diff(diff(diff(f(x, t), t), x), x), x))-72*f(x, t)^2*(diff(diff(diff(f(x, t), t), x), x))*(diff(f(x, t), x))^4+144*f(x, t)*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))^5+288*f(x, t)^3*(diff(f(x, t), t))*(diff(diff(f(x, t), x), x))*(diff(diff(f(x, t), t), x))*(diff(f(x, t), x))*b, x) = 0

(8)

``

(9)
 

``

Download int.mw

The XMLTools:-Validate function can be called with a reference to a schema.

I am a bit unsure where the schema location should be, especially if I can have the .xsd file in a library location.

Have done some tests, and as far as I can see, Maple does not give any error messages if the schema is not found at all. So I'm a bit unsure how to check if the schema defintion actually is read at all.

Something has changed in the past weeks (not sure for how long) and I have not figured out what exactly.

Probably it is me doing something differently while editing an input line. Below is an example where the name data is not italic any more

Anybody else experiencing the same?

My interface seetings:

 

Hi, I am searching for an exercise in MapleLearn, which I would like to give to my students in the second year of a mathematics degree. The aim is to make them work only with Maple Learn during 15-20 minutes. So the exercise should be rather short. The original idea that I had was to give them the Fibonacci sequence equation to solve : F(n+2)=F(n+1)+F(n). I would like to transform the sequence using a 2x2 matrix, which is classical. Diagonalize the matrix, compute the powers and so on. This is very easy with Maple, but how can I do that with MapleLearn? I could enter the corresponding  2x2 matrix, compute its eigenvalues but that's it. I could not diagonalize it, compute its powers and so on. Maybe someone knows how to do that with MapleLearn? Else I would be happy to discover other exercises with MapleLearn. 

Apart from introducing the software to french universities, the aim is also to make a research experiment (it is an official collaboration with Maplesoft)

The local command is really horribly treated in the manual. Very difficult to figure out heads from tails.

What follows is Maple code to unprotect the metric tensor g_[], and alter the components. that part I figured out by trial and error where the manual fails to clearly describe how.

But, the problem I now have, is that the unprotected metric does not show the tensor "visual matrix" form anymore if I execute  g_[] . So it makes it all unusable.

How do I enter the unprotected and altered g_[] back into maple so it can be used to calculate the Ricci tensor, Einstein tensor and such ? I guess it will have to be protected again etc. ?

Here is the code


restart;
with(Physics);
g_[sc];
g_[];
_local(g_[]);
g_[1, 2] := 1;
g_[3, 3];
Physics:-g_[1, 1];
g_[1, 2];
Physics:-g_[1, 1];
g_[];
for x to 4 do
    for y to 4 do g_[x, y] := Physics:-g_[x, y]; end do;
end do;
g_[];


So the question is. How do you reverse a localalized metric back to being protected after you altered the metric ?

How we can calculate solution of this ODE by give assumption to the equation , we have otehr case too, like lambda>0&mu<0

Hello Everyone,

I am wondring if I can  find the StandardRepresentation of a subalgebra of simple Lie algebra?

For example I have this code:

with(DifferentialGeometry);
with(LieAlgebras);
with(Library);
with(LinearAlgebra);

G := SimpleLieAlgebraData("sl(6)", sl6);
DGsetup(G);
StandardRepresentation(sl6);
M3 := MinimalSubalgebra([e30, e35, e20]);
B3 := LieAlgebraData(M3, p62);
Query("Jacobi");
DGsetup(B3);
StandardRepresentation(p62);
Error, (in DifferentialGeometry:-LieAlgebras:-StandardRepresentation) expected a Lie algebra constructed by the procedure SimpleLieAlgebraData
 

For the first StandardRepresentation(sl6); it works becouse of the definition. Now what I want the same idea for the subalgebra. How can I do that?

 

Any reason why the display of a fairly large plot in Maple 2024 (only show a print screen here)


be worst then the display of the same plot in Maple 2020

In 2024, it seams to be rasterized, while in 2020 it is still in vector form. Also the plot does not resize as well in 2024 compare to 2020. Any hint would help!

Maybe large plot are displayed in raster image, there is probably a setting somewhere in the documentation. When I export both are in vector format...

Thanks!

I experience Maple 2024 not beeing responsive.

It happens often that nothing is happening for 10 to 15 seconds after placing the cursor in an input line.

When the cursor is back, typing is normal for a little while and then again Maple is not reacting to user input.

The worksheets I am working with are between 50 and 100 Mb large in file size (containing plot3d structures, approx 1000 frames distributed across several plots:-display statements). It looks to me that the GUI has to do some house keeping from time to time which keeps it buisy with all the plot structures.

I could delete (plot) output, but this would require execution of the worksheet (before deleting the output) each time I want to continue working normally. This takes several minutes to be ready to work.

Anything else that I can do?

I am learning patten matching in Maple. 

Any one could explain why patmatch(1, (x::anything)^(n::'nonunit'(anything)))   gives true but patmatch(2, (x::anything)^n::'nonunit'(anything)); gives false?

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

restart;

patmatch(1, (x::anything)^(n::'nonunit'(anything)))

true

patmatch(2, (x::anything)^n::'nonunit'(anything));

false

Download patmatch_question_nov_16_2024.mw

I was expecting result similar to using this other software

I do not understand Maple's result. How could I change the patmatch so it does not match 1 to the pattern x::anything^n::anything where n is not 1 ?

Update

To give context, I was trying to write this example from the other software  in Maple:

But when I wrote this

expr:=1 + x^2 + x^4;

F:=proc(X::anything,x::symbol)
    local la,y,n;
    if patmatch(X, (y::anything)^(n::'nonunit'(anything)) ,'la') then  
       f(eval(n,la));
     else
        X;
     fi;
end proc;

map(X->F(X,x), expr);

Maple gave 

So I modified the code now to check for explicit 1,  to avoid this bad match, like this

expr:=1 + x^2 + x^4;

F:=proc(X::anything,x::symbol)
    local la,y,n;
    if patmatch(X, (y::anything)^(n::'nonunit'(anything)) ,'la') then  
        if eval(y,la)=1 then #bug in maple?
           X;
        else
           f(eval(n,la));
        fi;
     else
        X;
     fi;
end proc;

map(X->F(X,x), expr);

And now it gives expected result

How to insert a file inside another file, creating a session, without equations with the same name conflicting?

A farmer has exactly 100m of wire mesh fence available to enclose a pasture. The fence must begin and end at his large oak tree. To do this, imagine the usual "north-south/west-east" cross of the cardinal directions in the drawing plane. The oak tree is at the center of this.

1. All land that lies west of the imaginary axis is not worth a cent.

2. All land that lies east of the oak tree becomes continuously more expensive the further it is from the north-south axis. The property value is based on the function y = k · x, where y represents the price per square meter and x represents the distance in meters to the north-south axis. k is a proportionality factor, which for the task is k = 1 euro/m^3.

a) On which curve must the fence run so that the enclosed pasture area has the greatest possible value?

b) On which curve must the fence run if instead of the distance x from the north-south axis the distance r from the oak tree is decisive with the same factor k?

I was watching Maple's video for conference 2024. In one of the presentation, this example is given

But in my Mapple 2024.2 I get an error typing the same command:

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

restart;

my_ode:={diff(x(t),t$2)-t^2*x(t)=0, x(0)=1,D(x)(0)=1}:
MultivariatePowerSeries:-PowerSeries(my_ode,t,x);

Error, invalid input: too many and/or wrong type of arguments passed to MultivariatePowerSeries:-PowerSeries; first unused argument is t

 

 

Download powerSeries_nov_14_2024.mw

Link to the video is here  it is around 39:00 in time. 

Any one knows why I get an error using same command shown in the video?

I tried connecting Maple to Jupyter Notebook, but it seems that it is not keen on outputting everything within the for loop; it only outputs the last item.

for i from 1 to 24 do
    print(i);
end do;

I've noticed that the Maple interface is always white, and after a long time, it causes eye strain. I wonder if it's possible to adjust the interface color, similar to Mathematica. My system is Windows 11.

Currently, I often use VSCode as an alternative, but some mathematical symbols don't display very clearly.

I have noticed similar discussions, such as this one, but I don’t know how to do it

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