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Question: Formatting equations for LaTeX output

Question:Formatting equations for LaTeX output

salim-barzani 1395 Maple 2024
latex simplification
May 06 2025
0

I want to convert my code output into LaTeX format, but the current formatting isn't suitable for presentation. For example, when I use simplify, it sometimes introduces unnecessary fractions, making the expression look cluttered and less elegant on paper. I'm looking for a way to simplify expressions preferably by factoring terms, without introducing extra fractions, so the final LaTeX result appears clean and well-structured.

> 

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(u(x, t)); declare(U(xi)); declare(V(xi))

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

  

U(xi)*`will now be displayed as`*U

  

V(xi)*`will now be displayed as`*V

 (2)
> 

``
> 

RR := (2*v*(1/3)+2*alpha*beta*(1/3))*U(xi)^3+(-3*alpha*k^2*lambda-4*alpha^2*k-k^2*v+2*k^2*w-4*k*v*w)*U(xi)+(alpha*lambda+v)*(diff(diff(U(xi), xi), xi)) = 0

((2/3)*v+(2/3)*alpha*beta)*U(xi)^3+(-3*alpha*k^2*lambda-4*alpha^2*k-k^2*v+2*k^2*w-4*k*v*w)*U(xi)+(alpha*lambda+v)*(diff(diff(U(xi), xi), xi)) = 0

 (3)
> 

IM := -2*(diff(diff(U(xi), xi), xi))*v*k-2*U(xi)*k^2*w^2-2*(diff(diff(U(xi), xi), xi))*alpha^2+2*(diff(diff(U(xi), xi), xi))*v^2+(diff(diff(U(xi), xi), xi))*k*w+2*U(xi)^3*k*w-2*U(xi)^3*alpha*beta*k-3*(diff(diff(U(xi), xi), xi))*alpha*k*lambda-U(xi)*k^3*w+2*U(xi)*alpha^2*k^2+U(xi)*alpha*k^3*lambda = 0

-2*(diff(diff(U(xi), xi), xi))*v*k-2*U(xi)*k^2*w^2-2*(diff(diff(U(xi), xi), xi))*alpha^2+2*(diff(diff(U(xi), xi), xi))*v^2+(diff(diff(U(xi), xi), xi))*k*w+2*U(xi)^3*k*w-2*U(xi)^3*alpha*beta*k-3*(diff(diff(U(xi), xi), xi))*alpha*k*lambda-U(xi)*k^3*w+2*U(xi)*alpha^2*k^2+U(xi)*alpha*k^3*lambda = 0

 (4)
> 

collect(%, {U(xi), diff(diff(U(xi), xi), xi)})

(-2*alpha*beta*k+2*k*w)*U(xi)^3+(alpha*k^3*lambda+2*alpha^2*k^2-k^3*w-2*k^2*w^2)*U(xi)+(-3*alpha*k*lambda-2*alpha^2-2*k*v+k*w+2*v^2)*(diff(diff(U(xi), xi), xi)) = 0

 (5)
> 

P := %

(-2*alpha*beta*k+2*k*w)*U(xi)^3+(alpha*k^3*lambda+2*alpha^2*k^2-k^3*w-2*k^2*w^2)*U(xi)+(-3*alpha*k*lambda-2*alpha^2-2*k*v+k*w+2*v^2)*(diff(diff(U(xi), xi), xi)) = 0

 (6)
> 

NULL
> 

NULL
> 

C1 := v = solve(2*v*(1/3)+2*alpha*beta*(1/3) = 0, v)

v = -alpha*beta

 (7)
> 

C2 := k = solve(-3*alpha*k^2*lambda-4*alpha^2*k-k^2*v+2*k^2*w-4*k*v*w = 0, k)

k = (0, -4*(alpha^2+v*w)/(3*alpha*lambda+v-2*w))

 (8)
> 

C22 := subs(C1, C2)

k = (0, -4*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w))

 (9)
> 

C222 := k = -(4*(-alpha*beta*w+alpha^2))/(-alpha*beta+3*alpha*lambda-2*w)

k = -4*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)

 (10)
> 

ode := subs({C1, C222}, P)

(8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0

 (11)
> 

numer(lhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0))*denom(rhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0)) = numer(rhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0))*denom(lhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0))

-2*alpha*(-24*U(xi)^3*alpha^4*beta^2*lambda+36*U(xi)^3*alpha^4*beta*lambda^2-12*U(xi)^3*alpha^2*beta^3*w^2-16*U(xi)*alpha^4*beta^3*w^2-16*U(xi)*alpha^2*beta^3*w^4+9*(diff(diff(U(xi), xi), xi))*alpha^4*beta^4*lambda-27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3*lambda^2+27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda^3+12*U(xi)^3*alpha^3*beta^2*w-36*U(xi)^3*alpha^3*lambda^2*w+32*U(xi)*alpha^5*beta^2*w+32*U(xi)*alpha^3*beta^2*w^3+32*U(xi)*alpha*beta^2*w^5-2*(diff(diff(U(xi), xi), xi))*alpha^3*beta^4*w+48*U(xi)^3*alpha^2*lambda*w^2-16*U(xi)*alpha^4*beta*w^2-48*U(xi)*alpha^4*lambda*w^2-64*U(xi)*alpha^2*beta*w^4+21*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda-45*(diff(diff(U(xi), xi), xi))*alpha^4*beta*lambda^2+6*(diff(diff(U(xi), xi), xi))*alpha^2*beta^3*w^2-12*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*w-36*(diff(diff(U(xi), xi), xi))*alpha^3*lambda^2*w+16*(diff(diff(U(xi), xi), xi))*alpha*beta^2*w^3-12*(diff(diff(U(xi), xi), xi))*alpha^2*beta*w^2+12*(diff(diff(U(xi), xi), xi))*alpha^2*lambda*w^2-4*U(xi)^3*alpha^3*beta^4*w+24*U(xi)^3*alpha^3*beta^3*lambda*w-36*U(xi)^3*alpha^3*beta^2*lambda^2*w+32*U(xi)*alpha^3*beta^3*lambda*w^3+24*U(xi)^3*alpha^2*beta^2*lambda*w^2+36*U(xi)^3*alpha^2*beta*lambda^2*w^2-48*U(xi)*alpha^4*beta^2*lambda*w^2-48*U(xi)*alpha^2*beta^2*lambda*w^4-24*U(xi)^3*alpha^3*beta*lambda*w-48*U(xi)^3*alpha*beta*lambda*w^3+96*U(xi)*alpha^3*beta*lambda*w^3+6*(diff(diff(U(xi), xi), xi))*alpha^3*beta^3*lambda*w+18*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*lambda^2*w-54*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda^3*w-48*(diff(diff(U(xi), xi), xi))*alpha^2*beta^2*lambda*w^2+90*(diff(diff(U(xi), xi), xi))*alpha^2*beta*lambda^2*w^2+48*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda*w-48*(diff(diff(U(xi), xi), xi))*alpha*beta*lambda*w^3+4*U(xi)^3*alpha^4*beta^3-(diff(diff(U(xi), xi), xi))*alpha^4*beta^5+16*U(xi)^3*beta*w^4-16*U(xi)*alpha^6*beta+16*U(xi)*alpha^6*lambda-3*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3+27*(diff(diff(U(xi), xi), xi))*alpha^4*lambda^3-16*U(xi)^3*alpha*w^3+32*U(xi)*alpha^3*w^3+8*(diff(diff(U(xi), xi), xi))*beta*w^4) = 0

 (12)
> 

simplify(-2*alpha*(24*U(xi)^3*alpha^3*beta^3*lambda*w-36*U(xi)^3*alpha^3*beta^2*lambda^2*w+32*U(xi)*alpha^3*beta^3*lambda*w^3+24*U(xi)^3*alpha^2*beta^2*lambda*w^2+36*U(xi)^3*alpha^2*beta*lambda^2*w^2-48*U(xi)*alpha^4*beta^2*lambda*w^2-48*U(xi)*alpha^2*beta^2*lambda*w^4-24*U(xi)^3*alpha^3*beta*lambda*w-48*U(xi)^3*alpha*beta*lambda*w^3+96*U(xi)*alpha^3*beta*lambda*w^3+6*(diff(diff(U(xi), xi), xi))*alpha^3*beta^3*lambda*w+18*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*lambda^2*w-54*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda^3*w-48*(diff(diff(U(xi), xi), xi))*alpha^2*beta^2*lambda*w^2+90*(diff(diff(U(xi), xi), xi))*alpha^2*beta*lambda^2*w^2+48*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda*w-48*(diff(diff(U(xi), xi), xi))*alpha*beta*lambda*w^3-24*U(xi)^3*alpha^4*beta^2*lambda+36*U(xi)^3*alpha^4*beta*lambda^2-12*U(xi)^3*alpha^2*beta^3*w^2-16*U(xi)*alpha^4*beta^3*w^2-16*U(xi)*alpha^2*beta^3*w^4+9*(diff(diff(U(xi), xi), xi))*alpha^4*beta^4*lambda-27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3*lambda^2+27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda^3+12*U(xi)^3*alpha^3*beta^2*w-36*U(xi)^3*alpha^3*lambda^2*w+32*U(xi)*alpha^5*beta^2*w+32*U(xi)*alpha^3*beta^2*w^3+32*U(xi)*alpha*beta^2*w^5-2*(diff(diff(U(xi), xi), xi))*alpha^3*beta^4*w+48*U(xi)^3*alpha^2*lambda*w^2-16*U(xi)*alpha^4*beta*w^2-48*U(xi)*alpha^4*lambda*w^2-64*U(xi)*alpha^2*beta*w^4+21*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda-45*(diff(diff(U(xi), xi), xi))*alpha^4*beta*lambda^2+6*(diff(diff(U(xi), xi), xi))*alpha^2*beta^3*w^2-12*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*w-36*(diff(diff(U(xi), xi), xi))*alpha^3*lambda^2*w+16*(diff(diff(U(xi), xi), xi))*alpha*beta^2*w^3-12*(diff(diff(U(xi), xi), xi))*alpha^2*beta*w^2+12*(diff(diff(U(xi), xi), xi))*alpha^2*lambda*w^2-4*U(xi)^3*alpha^3*beta^4*w-(diff(diff(U(xi), xi), xi))*alpha^4*beta^5+4*U(xi)^3*alpha^4*beta^3+16*U(xi)^3*beta*w^4-16*U(xi)*alpha^6*beta+16*U(xi)*alpha^6*lambda-3*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3+27*(diff(diff(U(xi), xi), xi))*alpha^4*lambda^3-16*U(xi)^3*alpha*w^3+32*U(xi)*alpha^3*w^3+8*(diff(diff(U(xi), xi), xi))*beta*w^4) = 0)

-64*alpha*((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi)) = 0

 (13)
> 

%/(-64*alpha)

(1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0

 (14)
> 

PP := numer(lhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0))*denom(rhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0)) = numer(rhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0))*denom(lhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0))

-24*U(xi)^3*alpha^4*beta^2*lambda+36*U(xi)^3*alpha^4*beta*lambda^2-12*U(xi)^3*alpha^2*beta^3*w^2-16*U(xi)*alpha^4*beta^3*w^2-16*U(xi)*alpha^2*beta^3*w^4+9*(diff(diff(U(xi), xi), xi))*alpha^4*beta^4*lambda-27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3*lambda^2+27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda^3+12*U(xi)^3*alpha^3*beta^2*w-36*U(xi)^3*alpha^3*lambda^2*w+32*U(xi)*alpha^5*beta^2*w+32*U(xi)*alpha^3*beta^2*w^3+32*U(xi)*alpha*beta^2*w^5-2*(diff(diff(U(xi), xi), xi))*alpha^3*beta^4*w+48*U(xi)^3*alpha^2*lambda*w^2-16*U(xi)*alpha^4*beta*w^2-48*U(xi)*alpha^4*lambda*w^2-64*U(xi)*alpha^2*beta*w^4+21*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda-45*(diff(diff(U(xi), xi), xi))*alpha^4*beta*lambda^2+6*(diff(diff(U(xi), xi), xi))*alpha^2*beta^3*w^2-12*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*w-36*(diff(diff(U(xi), xi), xi))*alpha^3*lambda^2*w+16*(diff(diff(U(xi), xi), xi))*alpha*beta^2*w^3-12*(diff(diff(U(xi), xi), xi))*alpha^2*beta*w^2+12*(diff(diff(U(xi), xi), xi))*alpha^2*lambda*w^2-4*U(xi)^3*alpha^3*beta^4*w+24*U(xi)^3*alpha^3*beta^3*lambda*w-36*U(xi)^3*alpha^3*beta^2*lambda^2*w+32*U(xi)*alpha^3*beta^3*lambda*w^3+24*U(xi)^3*alpha^2*beta^2*lambda*w^2+36*U(xi)^3*alpha^2*beta*lambda^2*w^2-48*U(xi)*alpha^4*beta^2*lambda*w^2-48*U(xi)*alpha^2*beta^2*lambda*w^4-24*U(xi)^3*alpha^3*beta*lambda*w-48*U(xi)^3*alpha*beta*lambda*w^3+96*U(xi)*alpha^3*beta*lambda*w^3+6*(diff(diff(U(xi), xi), xi))*alpha^3*beta^3*lambda*w+18*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*lambda^2*w-54*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda^3*w-48*(diff(diff(U(xi), xi), xi))*alpha^2*beta^2*lambda*w^2+90*(diff(diff(U(xi), xi), xi))*alpha^2*beta*lambda^2*w^2+48*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda*w-48*(diff(diff(U(xi), xi), xi))*alpha*beta*lambda*w^3+4*U(xi)^3*alpha^4*beta^3-(diff(diff(U(xi), xi), xi))*alpha^4*beta^5+16*U(xi)^3*beta*w^4-16*U(xi)*alpha^6*beta+16*U(xi)*alpha^6*lambda-3*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3+27*(diff(diff(U(xi), xi), xi))*alpha^4*lambda^3-16*U(xi)^3*alpha*w^3+32*U(xi)*alpha^3*w^3+8*(diff(diff(U(xi), xi), xi))*beta*w^4 = 0

 (15)
> 

NULL
> 

collect(PP, {U(xi), diff(U(xi), xi), diff(diff(U(xi), xi), xi)})

(-4*alpha^3*beta^4*w+24*alpha^3*beta^3*lambda*w-36*alpha^3*beta^2*lambda^2*w+4*alpha^4*beta^3-24*alpha^4*beta^2*lambda+36*alpha^4*beta*lambda^2-12*alpha^2*beta^3*w^2+24*alpha^2*beta^2*lambda*w^2+36*alpha^2*beta*lambda^2*w^2+12*alpha^3*beta^2*w-24*alpha^3*beta*lambda*w-36*alpha^3*lambda^2*w-48*alpha*beta*lambda*w^3+48*alpha^2*lambda*w^2+16*beta*w^4-16*alpha*w^3)*U(xi)^3+(32*alpha^3*beta^3*lambda*w^3-16*alpha^4*beta^3*w^2-48*alpha^4*beta^2*lambda*w^2-16*alpha^2*beta^3*w^4-48*alpha^2*beta^2*lambda*w^4+32*alpha^5*beta^2*w+32*alpha^3*beta^2*w^3+96*alpha^3*beta*lambda*w^3+32*alpha*beta^2*w^5-16*alpha^6*beta+16*alpha^6*lambda-16*alpha^4*beta*w^2-48*alpha^4*lambda*w^2-64*alpha^2*beta*w^4+32*alpha^3*w^3)*U(xi)+(-alpha^4*beta^5+9*alpha^4*beta^4*lambda-27*alpha^4*beta^3*lambda^2+27*alpha^4*beta^2*lambda^3-2*alpha^3*beta^4*w+6*alpha^3*beta^3*lambda*w+18*alpha^3*beta^2*lambda^2*w-54*alpha^3*beta*lambda^3*w-3*alpha^4*beta^3+21*alpha^4*beta^2*lambda-45*alpha^4*beta*lambda^2+27*alpha^4*lambda^3+6*alpha^2*beta^3*w^2-48*alpha^2*beta^2*lambda*w^2+90*alpha^2*beta*lambda^2*w^2-12*alpha^3*beta^2*w+48*alpha^3*beta*lambda*w-36*alpha^3*lambda^2*w+16*alpha*beta^2*w^3-48*alpha*beta*lambda*w^3-12*alpha^2*beta*w^2+12*alpha^2*lambda*w^2+8*beta*w^4)*(diff(diff(U(xi), xi), xi)) = 0

 (16)
 

NULL

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