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Question: How finding parameter, in somewhere i did mistake i can't recognize where ?

Question:How finding parameter, in somewhere i did mistake i can't recognize where ?

salim-barzani 925 Maple 2024
syntax pde differential-equations coefficients
April 10 2025
2

This is first type of solving parameter but  i solved some semilar but the shape of them are so different and solving them different too i did my trail but i can't reach out solution also the author solve by another way which i did too but i have to solve in this way too thanks  for any help !

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

``

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

 (1)
> 

declare(u(x, y, z, t))

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

 (2)
> 

declare(f(x, y, z, t))

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

 (3)
> 

pde := 9*(diff(u(x, y, z, t), t, x))+diff(u(x, y, z, t), `$`(x, 6))-5*(diff(u(x, y, z, t), `$`(x, 3), y)+diff(u(x, y, z, t), `$`(y, 2)))+15*((diff(u(x, y, z, t), `$`(x, 2)))*(diff(u(x, y, z, t), `$`(x, 3)))+(diff(u(x, y, z, t), x))*(diff(u(x, y, z, t), `$`(x, 4)))-(diff(u(x, y, z, t), x))*(diff(u(x, y, z, t), x, y))-(diff(u(x, y, z, t), `$`(x, 2)))*(diff(u(x, y, z, t), y)))+45*(diff(u(x, y, z, t), x))^2*(diff(u(x, y, z, t), `$`(x, 2)))+alpha*(diff(u(x, y, z, t), `$`(x, 2)))+beta*(diff(u(x, y, z, t), x, y))+delta*(diff(u(x, y, z, t), x, z))

9*(diff(diff(u(x, y, z, t), t), x))+diff(diff(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x), x), x)-5*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), y))-5*(diff(diff(u(x, y, z, t), y), y))+15*(diff(diff(u(x, y, z, t), x), x))*(diff(diff(diff(u(x, y, z, t), x), x), x))+15*(diff(u(x, y, z, t), x))*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-15*(diff(u(x, y, z, t), x))*(diff(diff(u(x, y, z, t), x), y))-15*(diff(diff(u(x, y, z, t), x), x))*(diff(u(x, y, z, t), y))+45*(diff(u(x, y, z, t), x))^2*(diff(diff(u(x, y, z, t), x), x))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+delta*(diff(diff(u(x, y, z, t), x), z))

 (4)
> 

``
> 

oppde := [op(expand(pde))]; u_occurrences := map(proc (i) options operator, arrow; numelems(select(has, [op([op(i)])], u)) end proc, oppde); linear_op_indices := ListTools:-SearchAll(1, u_occurrences); pde_linear := add(oppde[[linear_op_indices]]); pde_nonlinear := expand(simplify(expand(pde)-pde_linear))

9*(diff(diff(u(x, y, z, t), t), x))+diff(diff(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x), x), x)-5*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), y))-5*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+delta*(diff(diff(u(x, y, z, t), x), z))

  

15*(diff(diff(u(x, y, z, t), x), x))*(diff(diff(diff(u(x, y, z, t), x), x), x))+15*(diff(u(x, y, z, t), x))*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-15*(diff(u(x, y, z, t), x))*(diff(diff(u(x, y, z, t), x), y))-15*(diff(diff(u(x, y, z, t), x), x))*(diff(u(x, y, z, t), y))+45*(diff(u(x, y, z, t), x))^2*(diff(diff(u(x, y, z, t), x), x))

 (5)
> 

H := u(x, y, z, t) = 2*(diff(ln(f(x, y, z, t)), x))

u(x, y, z, t) = 2*(diff(f(x, y, z, t), x))/f(x, y, z, t)

 (6)
> 

L := eval(pde_linear, H) = 0

2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t) = 0

 (7)
> 

numer(lhs(-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2 = 0))*denom(rhs(-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2 = 0)) = numer(rhs(-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2 = 0))*denom(lhs(-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2 = 0))

420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^4-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^3-6*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*alpha-2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))*beta-4*f(x, y, z, t)^5*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))*beta+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))*beta-2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))*delta-4*f(x, y, z, t)^5*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))*delta+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))*delta-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^4+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))*f(x, y, z, t)^6-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))*f(x, y, z, t)^6-10*(diff(diff(diff(f(x, y, z, t), x), y), y))*f(x, y, z, t)^6+18*(diff(diff(diff(f(x, y, z, t), t), x), x))*f(x, y, z, t)^6-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^5-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))*f(x, y, z, t)^5+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^5+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^5-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))*f(x, y, z, t)^5-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^5+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5*f(x, y, z, t)+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))*f(x, y, z, t)^3-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^4-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^3+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)^2+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2*f(x, y, z, t)^4+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))*f(x, y, z, t)^4-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))*f(x, y, z, t)^5+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), x))*alpha+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^3*alpha+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), y))*beta+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), z))*delta+1440*(diff(f(x, y, z, t), x))^7 = 0

 (8)
> 

F1 := %

420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^4-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^3-6*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*alpha-2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))*beta-4*f(x, y, z, t)^5*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))*beta+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))*beta-2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))*delta-4*f(x, y, z, t)^5*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))*delta+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))*delta-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^4+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))*f(x, y, z, t)^6-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))*f(x, y, z, t)^6-10*(diff(diff(diff(f(x, y, z, t), x), y), y))*f(x, y, z, t)^6+18*(diff(diff(diff(f(x, y, z, t), t), x), x))*f(x, y, z, t)^6-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^5-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))*f(x, y, z, t)^5+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^5+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^5-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))*f(x, y, z, t)^5-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^5+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5*f(x, y, z, t)+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))*f(x, y, z, t)^3-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^4-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^3+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)^2+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2*f(x, y, z, t)^4+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))*f(x, y, z, t)^4-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))*f(x, y, z, t)^5+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), x))*alpha+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^3*alpha+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), y))*beta+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), z))*delta+1440*(diff(f(x, y, z, t), x))^7 = 0

 (9)
> 

NULL
> 

S := f(x, y, z, t) = a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])

f(x, y, z, t) = a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])

 (10)
> 

A := eval(F1, S)

600*a[1]^4*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3+1204*a[1]^3*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4-4200*a[1]^4*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3-500*a[1]^3*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+30*a[1]^2*k[1]*p[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-54*a[1]^2*w[1]*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^3*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*alpha-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*p[1]*beta+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]*beta-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*r[1]*delta+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*r[1]*delta+18*a[1]*w[1]*k[1]^2*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-10*a[1]*k[1]*p[1]^2*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6+2*a[1]*k[1]^7*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-10*a[1]*k[1]^4*p[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^2*p[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*beta+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^2*r[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*delta+1440*a[1]^7*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^7-5040*a[1]^6*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))+6720*a[1]^5*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2-20*a[1]^3*k[1]*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+36*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*w[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^3*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*alpha+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^3*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*alpha-126*a[1]^2*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5+150*a[1]^2*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-240*a[1]^5*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2 = 0

 (11)
> 

simplify(1440*a[1]^7*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^7+6720*a[1]^5*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2-126*a[1]^2*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5+1204*a[1]^3*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4-4200*a[1]^4*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3+2*a[1]*k[1]^7*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-5040*a[1]^6*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))+600*a[1]^4*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3-500*a[1]^3*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+30*a[1]^2*k[1]*p[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-54*a[1]^2*w[1]*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^3*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*alpha+18*a[1]*w[1]*k[1]^2*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-10*a[1]*k[1]*p[1]^2*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-10*a[1]*k[1]^4*p[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-20*a[1]^3*k[1]*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+36*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*w[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^3*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*alpha+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^3*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*alpha+150*a[1]^2*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-240*a[1]^5*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*p[1]*beta+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]*beta-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*r[1]*delta+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*r[1]*delta+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^2*p[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*beta+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^2*r[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*delta = 0)

2*a[0]*k[1]*(-57*a[0]^4*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]*exp(2*t*w[1]+2*x*k[1]+2*y*p[1]+2*z*r[1])+302*a[0]^3*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^2*exp(3*t*w[1]+3*x*k[1]+3*y*p[1]+3*z*r[1])-302*a[0]^2*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^3*exp(4*t*w[1]+4*x*k[1]+4*y*p[1]+4*z*r[1])+57*a[0]*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]^4*exp(5*t*w[1]+5*x*k[1]+5*y*p[1]+5*z*r[1])+(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*a[0]^5-exp(6*t*w[1]+6*x*k[1]+6*y*p[1]+6*z*r[1])*a[1]^5)*(k[1]^6-5*k[1]^3*p[1]+k[1]^2*alpha+(beta*p[1]+delta*r[1]+9*w[1])*k[1]-5*p[1]^2))*a[1] = 0

 (12)
> 

E := %

2*a[0]*k[1]*(-57*a[0]^4*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]*exp(2*t*w[1]+2*x*k[1]+2*y*p[1]+2*z*r[1])+302*a[0]^3*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^2*exp(3*t*w[1]+3*x*k[1]+3*y*p[1]+3*z*r[1])-302*a[0]^2*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^3*exp(4*t*w[1]+4*x*k[1]+4*y*p[1]+4*z*r[1])+57*a[0]*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]^4*exp(5*t*w[1]+5*x*k[1]+5*y*p[1]+5*z*r[1])+(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*a[0]^5-exp(6*t*w[1]+6*x*k[1]+6*y*p[1]+6*z*r[1])*a[1]^5)*(k[1]^6-5*k[1]^3*p[1]+k[1]^2*alpha+(beta*p[1]+delta*r[1]+9*w[1])*k[1]-5*p[1]^2))*a[1] = 0

 (13)
> 

indets(E)

{alpha, beta, delta, t, x, y, z, a[0], a[1], k[1], p[1], r[1], w[1], exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]), exp(2*t*w[1]+2*x*k[1]+2*y*p[1]+2*z*r[1]), exp(3*t*w[1]+3*x*k[1]+3*y*p[1]+3*z*r[1]), exp(4*t*w[1]+4*x*k[1]+4*y*p[1]+4*z*r[1]), exp(5*t*w[1]+5*x*k[1]+5*y*p[1]+5*z*r[1]), exp(6*t*w[1]+6*x*k[1]+6*y*p[1]+6*z*r[1])}

 (14)
> 

E1 := subs({exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]) = eX, exp(2*t*w[1]+2*x*k[1]+2*y*p[1]+2*z*r[1]) = eY, exp(3*t*w[1]+3*x*k[1]+3*y*p[1]+3*z*r[1]) = eZ, exp(4*t*w[1]+4*x*k[1]+4*y*p[1]+4*z*r[1]) = eW, exp(5*t*w[1]+5*x*k[1]+5*y*p[1]+5*z*r[1]) = eV, exp(6*t*w[1]+6*x*k[1]+6*y*p[1]+6*z*r[1]) = eB}, E)

2*a[0]*k[1]*(-57*a[0]^4*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]*eY+302*a[0]^3*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^2*eZ-302*a[0]^2*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^3*eW+57*a[0]*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]^4*eV+(-eB*a[1]^5+eX*a[0]^5)*(k[1]^6-5*k[1]^3*p[1]+k[1]^2*alpha+(beta*p[1]+delta*r[1]+9*w[1])*k[1]-5*p[1]^2))*a[1] = 0

 (15)
> 

indets(E1)

{alpha, beta, delta, eB, eV, eW, eX, eY, eZ, a[0], a[1], k[1], p[1], r[1], w[1]}

 (16)
> 

p2c := normal(E1)

-2*a[0]*k[1]*(eB*a[1]^5*k[1]^6-57*eV*a[0]*a[1]^4*k[1]^6+302*eW*a[0]^2*a[1]^3*k[1]^6-eX*a[0]^5*k[1]^6+57*eY*a[0]^4*a[1]*k[1]^6-302*eZ*a[0]^3*a[1]^2*k[1]^6-5*eB*a[1]^5*k[1]^3*p[1]+45*eV*a[0]*a[1]^4*k[1]^3*p[1]+50*eW*a[0]^2*a[1]^3*k[1]^3*p[1]+5*eX*a[0]^5*k[1]^3*p[1]-45*eY*a[0]^4*a[1]*k[1]^3*p[1]-50*eZ*a[0]^3*a[1]^2*k[1]^3*p[1]+alpha*eB*a[1]^5*k[1]^2+3*alpha*eV*a[0]*a[1]^4*k[1]^2+2*alpha*eW*a[0]^2*a[1]^3*k[1]^2-alpha*eX*a[0]^5*k[1]^2-3*alpha*eY*a[0]^4*a[1]*k[1]^2-2*alpha*eZ*a[0]^3*a[1]^2*k[1]^2+beta*eB*a[1]^5*k[1]*p[1]+3*beta*eV*a[0]*a[1]^4*k[1]*p[1]+2*beta*eW*a[0]^2*a[1]^3*k[1]*p[1]-beta*eX*a[0]^5*k[1]*p[1]-3*beta*eY*a[0]^4*a[1]*k[1]*p[1]-2*beta*eZ*a[0]^3*a[1]^2*k[1]*p[1]+delta*eB*a[1]^5*k[1]*r[1]+3*delta*eV*a[0]*a[1]^4*k[1]*r[1]+2*delta*eW*a[0]^2*a[1]^3*k[1]*r[1]-delta*eX*a[0]^5*k[1]*r[1]-3*delta*eY*a[0]^4*a[1]*k[1]*r[1]-2*delta*eZ*a[0]^3*a[1]^2*k[1]*r[1]+9*eB*a[1]^5*k[1]*w[1]-5*eB*a[1]^5*p[1]^2+27*eV*a[0]*a[1]^4*k[1]*w[1]-15*eV*a[0]*a[1]^4*p[1]^2+18*eW*a[0]^2*a[1]^3*k[1]*w[1]-10*eW*a[0]^2*a[1]^3*p[1]^2-9*eX*a[0]^5*k[1]*w[1]+5*eX*a[0]^5*p[1]^2-27*eY*a[0]^4*a[1]*k[1]*w[1]+15*eY*a[0]^4*a[1]*p[1]^2-18*eZ*a[0]^3*a[1]^2*k[1]*w[1]+10*eZ*a[0]^3*a[1]^2*p[1]^2)*a[1] = 0

 (17)
> 

indets(p2c)

{alpha, beta, delta, eB, eV, eW, eX, eY, eZ, a[0], a[1], k[1], p[1], r[1], w[1]}

 (18)
> 

eqns := {coeffs(collect(p2c, {eB, eV, eW, eX, eY, eZ}, distributed), {eB, eV, eW, eX, eY, eZ})}; nops(%)

Error, invalid arguments to coeffs

  

1

 (19)
> 

NULL
> 

Co := solve(E1, {a[0], a[1], k[1], n[1], p[1], r[1], w[1]}, explicit)

{a[0] = a[0], a[1] = a[1], k[1] = 0, n[1] = n[1], p[1] = p[1], r[1] = r[1], w[1] = w[1]}, {a[0] = a[0], a[1] = 0, k[1] = k[1], n[1] = n[1], p[1] = p[1], r[1] = r[1], w[1] = w[1]}, {a[0] = 0, a[1] = a[1], k[1] = k[1], n[1] = n[1], p[1] = p[1], r[1] = r[1], w[1] = w[1]}, {a[0] = a[0], a[1] = a[1], k[1] = k[1], n[1] = n[1], p[1] = p[1], r[1] = -(eB*a[1]^5*k[1]^6-57*eV*a[0]*a[1]^4*k[1]^6+302*eW*a[0]^2*a[1]^3*k[1]^6-eX*a[0]^5*k[1]^6+57*eY*a[0]^4*a[1]*k[1]^6-302*eZ*a[0]^3*a[1]^2*k[1]^6-5*eB*a[1]^5*k[1]^3*p[1]+45*eV*a[0]*a[1]^4*k[1]^3*p[1]+50*eW*a[0]^2*a[1]^3*k[1]^3*p[1]+5*eX*a[0]^5*k[1]^3*p[1]-45*eY*a[0]^4*a[1]*k[1]^3*p[1]-50*eZ*a[0]^3*a[1]^2*k[1]^3*p[1]+alpha*eB*a[1]^5*k[1]^2+3*alpha*eV*a[0]*a[1]^4*k[1]^2+2*alpha*eW*a[0]^2*a[1]^3*k[1]^2-alpha*eX*a[0]^5*k[1]^2-3*alpha*eY*a[0]^4*a[1]*k[1]^2-2*alpha*eZ*a[0]^3*a[1]^2*k[1]^2+beta*eB*a[1]^5*k[1]*p[1]+3*beta*eV*a[0]*a[1]^4*k[1]*p[1]+2*beta*eW*a[0]^2*a[1]^3*k[1]*p[1]-beta*eX*a[0]^5*k[1]*p[1]-3*beta*eY*a[0]^4*a[1]*k[1]*p[1]-2*beta*eZ*a[0]^3*a[1]^2*k[1]*p[1]+9*eB*a[1]^5*k[1]*w[1]-5*eB*a[1]^5*p[1]^2+27*eV*a[0]*a[1]^4*k[1]*w[1]-15*eV*a[0]*a[1]^4*p[1]^2+18*eW*a[0]^2*a[1]^3*k[1]*w[1]-10*eW*a[0]^2*a[1]^3*p[1]^2-9*eX*a[0]^5*k[1]*w[1]+5*eX*a[0]^5*p[1]^2-27*eY*a[0]^4*a[1]*k[1]*w[1]+15*eY*a[0]^4*a[1]*p[1]^2-18*eZ*a[0]^3*a[1]^2*k[1]*w[1]+10*eZ*a[0]^3*a[1]^2*p[1]^2)/(delta*k[1]*(eB*a[1]^5+3*eV*a[0]*a[1]^4+2*eW*a[0]^2*a[1]^3-eX*a[0]^5-3*eY*a[0]^4*a[1]-2*eZ*a[0]^3*a[1]^2)), w[1] = w[1]}

 (20)
> 

NULL
> 

case1 := Co[1]

{a[0] = a[0], a[1] = a[1], k[1] = 0, n[1] = n[1], p[1] = p[1], r[1] = r[1], w[1] = w[1]}

 (21)
> 

F := subs(case1, S)

f(x, y, z, t) = a[0]+a[1]*exp(t*w[1]+y*p[1]+z*r[1])

 (22)
> 

F1 := eval(H, F)

u(x, y, z, t) = 0

 (23)
> 

NULL
> 

pdetest(F1, pde)

0

 (24)

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