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salim-barzani

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These are questions asked by salim-barzani

Help with Solving ODE and Representing &...

salim-barzani 1640 Maple 2024
ode dsolve differential-equations
April 29 2025
2 6

I tried solving this ODE, but my result is very different from the expected one. How can I correctly obtain the solution? Also, is there a way to include both the positive and negative signs (±) in the equation so that the final result reflects both possibilities?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

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

 (1)
> 

_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.

  
> 

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

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

  

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

  

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

  

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

  

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

 (2)
> 

``
> 

ode := f*g^3*(diff(diff(U(xi), xi), xi))-4*f*p*U(xi)-6*k*l*U(xi)-f^3*g*(diff(diff(U(xi), xi), xi))+6*f*g*U(xi)^2 = 0

f*g^3*(diff(diff(U(xi), xi), xi))-4*f*p*U(xi)-6*k*l*U(xi)-f^3*g*(diff(diff(U(xi), xi), xi))+6*f*g*U(xi)^2 = 0

 (3)
> 

S := (diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

(diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

 (4)
> 

S1 := dsolve(S, G(xi))

G(xi) = (1/2)*(-b+(-4*a*l+b^2)^(1/2))/l, G(xi) = -(1/2)*(b+(-4*a*l+b^2)^(1/2))/l, G(xi) = -4*a*exp(c__1*r*a^(1/2))/(exp(xi*r*a^(1/2))*(4*a*l-b^2+2*b*exp(c__1*r*a^(1/2))/exp(xi*r*a^(1/2))-(exp(c__1*r*a^(1/2)))^2/(exp(xi*r*a^(1/2)))^2)), G(xi) = -4*a*exp(xi*r*a^(1/2))/(exp(c__1*r*a^(1/2))*(4*a*l-b^2+2*b*exp(xi*r*a^(1/2))/exp(c__1*r*a^(1/2))-(exp(xi*r*a^(1/2)))^2/(exp(c__1*r*a^(1/2)))^2))

 (5)
> 

S2 := S1[3]

G(xi) = -4*a*exp(c__1*r*a^(1/2))/(exp(xi*r*a^(1/2))*(4*a*l-b^2+2*b*exp(c__1*r*a^(1/2))/exp(xi*r*a^(1/2))-(exp(c__1*r*a^(1/2)))^2/(exp(xi*r*a^(1/2)))^2))

 (6)
> 

normal(G(xi) = -4*a*exp(c__1*r*a^(1/2))/(exp(xi*r*a^(1/2))*(4*a*l-b^2+2*b*exp(c__1*r*a^(1/2))/exp(xi*r*a^(1/2))-(exp(c__1*r*a^(1/2)))^2/(exp(xi*r*a^(1/2)))^2)), ':-expanded')

G(xi) = 4*a*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))/(-4*a*l*(exp(xi*r*a^(1/2)))^2+b^2*(exp(xi*r*a^(1/2)))^2-2*b*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))+(exp(c__1*r*a^(1/2)))^2)

 (7)
> 

simplify(G(xi) = 4*a*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))/(-4*a*l*(exp(xi*r*a^(1/2)))^2+b^2*(exp(xi*r*a^(1/2)))^2-2*b*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))+(exp(c__1*r*a^(1/2)))^2))

G(xi) = -4*a*exp(a^(1/2)*r*(c__1+xi))/(4*a*l*exp(2*xi*r*a^(1/2))-b^2*exp(2*xi*r*a^(1/2))+2*b*exp(a^(1/2)*r*(c__1+xi))-exp(2*c__1*r*a^(1/2)))

 (8)
> 

convert(%, trig)

G(xi) = -4*a*(cosh(a^(1/2)*r*(c__1+xi))+sinh(a^(1/2)*r*(c__1+xi)))/(4*a*l*(cosh(2*xi*r*a^(1/2))+sinh(2*xi*r*a^(1/2)))-b^2*(cosh(2*xi*r*a^(1/2))+sinh(2*xi*r*a^(1/2)))+2*b*(cosh(a^(1/2)*r*(c__1+xi))+sinh(a^(1/2)*r*(c__1+xi)))-cosh(2*c__1*r*a^(1/2))-sinh(2*c__1*r*a^(1/2)))

 (9)
> 

convert(S1[3], trig)

G(xi) = -4*a*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/((cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))*(4*a*l-b^2+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))-(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))^2/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))^2))

 (10)
> 

simplify(G(xi) = -4*a*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/((cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))*(4*a*l-b^2+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))-(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))^2/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))^2)))

G(xi) = -4*a*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))*(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))/((4*a*l-b^2)*cosh(xi*r*a^(1/2))^2+((8*a*l-2*b^2)*sinh(xi*r*a^(1/2))+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2))))*cosh(xi*r*a^(1/2))+(4*a*l-b^2)*sinh(xi*r*a^(1/2))^2+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))*sinh(xi*r*a^(1/2))-(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))^2)

 (11)
   

Download tt.mw

Controlling Variable Distribution in Pol...

salim-barzani 1640 Maple 2024
polynomial expand pde
April 28 2025
1 4

In this work, I do not intend to expand all the variables across the monomials. Instead, I want to restrict the distribution to only the variables x,y,z,tx, y, z, tx,y,z,t, possibly raising them to appropriate powers as needed, until I obtain the desired solution and satisfy the conditions of my PDE tests. However, I am uncertain whether "monomial" is the correct term to use here.

S1.mw

trail-1.mw

Separating solutions based on PDE satisf...

salim-barzani 1640 Maple 2024
pde differential-equations select
April 27 2025
1 5

I have a list of candidate solutions. Some of them satisfy my PDE test (i.e., they make the PDE equal to zero), while others do not. How can I separate the solutions that satisfy the PDE from those that do not?

Trail-pdetest.mw

Modifying an Algorithm for Multiple Vari...

salim-barzani 1640 Maple 2024
differentiation duplicate-question
April 27 2025
1 8

How to modify the ND procedure to handle derivatives with respect to more than three independent variables for higher-dimensional PDEs, it is work for [x,t] i want  it work for [x,y,z,t] , 

> 

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)
> 

alias(F=F(x, t), G=G(x, t))

F, G

 (2)
> 

with(PDEtools):
undeclare(prime):

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

 (3)
> 

ND := proc(F, G, U)
  local v, w, f, g, a:
  v := op(F):
  if v[1] in U then w := -v[1] else w := v[1] end if:
  if v[2] in U then w := w, -v[2] else w := w, v[2] end if:
  f := op(0, F):
  g := op(0, G):
  a := diff(f(w)*g(v), U);
  convert(subs([w]=~[v], a), diff)
end proc:
> 

ND(F, G, [x]);
ND(F, G, [t]);

-(diff(F, x))*G+F*(diff(G, x))

  

-(diff(F, t))*G+F*(diff(G, t))

 (4)
> 

ND(F, F, [x]);
ND(F, F, [x, x]);

0

  

2*F*(diff(diff(F, x), x))-2*(diff(F, x))^2

 (5)
> 

ND(F, G, [x$3]);

-(diff(diff(diff(F, x), x), x))*G+3*(diff(diff(F, x), x))*(diff(G, x))-3*(diff(F, x))*(diff(diff(G, x), x))+F*(diff(diff(diff(G, x), x), x))

 (6)
> 

ND(F, F, [x$3, t]);

2*F*(diff(diff(diff(diff(F, t), x), x), x))-2*(diff(diff(diff(F, x), x), x))*(diff(F, t))-6*(diff(diff(diff(F, t), x), x))*(diff(F, x))+6*(diff(diff(F, x), x))*(diff(diff(F, t), x))

 (7)
> 

NULL
> 

NULL
> 

#if i collect P1+P1+...+P7 it must get equation 26 in paper so i want define the up proc to open but is not for (3+1) dimesnion,
> 

P1 := 9*ND(F, F, [x, t])

18*F*(diff(diff(F, t), x))-18*(diff(F, x))*(diff(F, t))

 (8)
> 

NULL
> 

P2 := -5*ND(F, F, [`$`(x, 3), y])

0

 (9)
> 

P3 := ND(F, F, [`$`(x, 6)])

2*F*(diff(diff(diff(diff(diff(diff(F, x), x), x), x), x), x))-12*(diff(diff(diff(diff(diff(F, x), x), x), x), x))*(diff(F, x))+30*(diff(diff(diff(diff(F, x), x), x), x))*(diff(diff(F, x), x))-20*(diff(diff(diff(F, x), x), x))^2

 (10)
> 

P4 := -5*ND(F, F, [`$`(y, 2)])

0

 (11)
> 

P5 := alpha*ND(F, F, [`$`(x, 2)])

alpha*(2*F*(diff(diff(F, x), x))-2*(diff(F, x))^2)

 (12)
> 

P6 := beta*ND(F, F, [x, y])

0

 (13)
> 

P7 := gamma*ND(F, F, [x, z])

0

 (14)

Download define.mw

How build up a system of equations of th...

salim-barzani 1640 Maple 2024
parameters substitution pde
April 26 2025
2 12

I try to construct a system of coefficient but  i don't know why distribute of them is not working, beside this there is any other way for build this kind of systems 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

_local(gamma)
> 

``

`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)
> 

H1 := int(pde_linear, x)

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

 (7)
> 

L := eval(H1, H) = 0

-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+240*(diff(diff(diff(f(x, y, z, t), 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+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(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(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2)+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t) = 0

 (8)
> 

numer(lhs(240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^4+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t)+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2) = 0))*denom(rhs(240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^4+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t)+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2) = 0)) = numer(rhs(240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^4+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t)+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2) = 0))*denom(lhs(240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^4+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t)+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2) = 0))

2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*alpha+2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), y))*beta+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^3-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^2-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))*f(x, y, z, t)^4-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^4+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^4+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+2*(diff(diff(f(x, y, z, t), x), z))*delta*f(x, y, z, t)^5+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2-2*(diff(f(x, y, z, t), x))^2*alpha*f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^6-2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4*(diff(f(x, y, z, t), y))*beta-2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4*(diff(f(x, y, z, t), z))*delta+240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*f(x, y, z, t)^5-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*f(x, y, z, t)^5-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))^3*f(x, y, z, t)^3+18*(diff(diff(f(x, y, z, t), t), x))*f(x, y, z, t)^5-10*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5+10*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4 = 0

 (9)
> 

simplify(2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*f(x, y, z, t)^5-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*f(x, y, z, t)^5-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))^3*f(x, y, z, t)^3+18*(diff(diff(f(x, y, z, t), t), x))*f(x, y, z, t)^5-10*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5+10*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4+2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), y))*beta+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^3-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^2-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))*f(x, y, z, t)^4-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^4+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^4+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+2*(diff(diff(f(x, y, z, t), x), z))*delta*f(x, y, z, t)^5+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2-2*(diff(f(x, y, z, t), x))^2*alpha*f(x, y, z, t)^4+2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*alpha-240*(diff(f(x, y, z, t), x))^6-2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4*(diff(f(x, y, z, t), y))*beta-2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4*(diff(f(x, y, z, t), z))*delta+240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3 = 0)

2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*f(x, y, z, t)^5-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+30*(2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3-f(x, y, z, t)^4*(diff(diff(f(x, y, z, t), x), x)))*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*f(x, y, z, t)^5-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*f(x, y, z, t)^4+10*(-24*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2+24*(diff(f(x, y, z, t), x))*f(x, y, z, t)^3*(diff(diff(f(x, y, z, t), x), x))+(diff(f(x, y, z, t), y))*f(x, y, z, t)^4)*(diff(diff(diff(f(x, y, z, t), x), x), x))+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))^3*f(x, y, z, t)^3-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^2+2*(alpha*f(x, y, z, t)^5+360*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-30*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3*(diff(f(x, y, z, t), x))+15*f(x, y, z, t)^4*(diff(diff(f(x, y, z, t), x), y)))*(diff(diff(f(x, y, z, t), x), x))+2*(beta*f(x, y, z, t)^5-30*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3)*(diff(diff(f(x, y, z, t), x), y))+18*(diff(diff(f(x, y, z, t), t), x))*f(x, y, z, t)^5+2*(diff(diff(f(x, y, z, t), x), z))*delta*f(x, y, z, t)^5-10*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5-240*(diff(f(x, y, z, t), x))^6+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2-2*(diff(f(x, y, z, t), x))^2*alpha*f(x, y, z, t)^4-2*f(x, y, z, t)^4*(beta*(diff(f(x, y, z, t), y))+(diff(f(x, y, z, t), z))*delta+9*(diff(f(x, y, z, t), t)))*(diff(f(x, y, z, t), x))+10*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4 = 0

 (10)
> 

F1 := %*(1/2)

(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*f(x, y, z, t)^5-6*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+15*(2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3-f(x, y, z, t)^4*(diff(diff(f(x, y, z, t), x), x)))*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))-5*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*f(x, y, z, t)^5-10*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*f(x, y, z, t)^4+5*(-24*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2+24*(diff(f(x, y, z, t), x))*f(x, y, z, t)^3*(diff(diff(f(x, y, z, t), x), x))+(diff(f(x, y, z, t), y))*f(x, y, z, t)^4)*(diff(diff(diff(f(x, y, z, t), x), x), x))+15*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+30*(diff(diff(f(x, y, z, t), x), x))^3*f(x, y, z, t)^3-270*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^2+(alpha*f(x, y, z, t)^5+360*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-30*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3*(diff(f(x, y, z, t), x))+15*f(x, y, z, t)^4*(diff(diff(f(x, y, z, t), x), y)))*(diff(diff(f(x, y, z, t), x), x))+(beta*f(x, y, z, t)^5-30*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3)*(diff(diff(f(x, y, z, t), x), y))+9*(diff(diff(f(x, y, z, t), t), x))*f(x, y, z, t)^5+(diff(diff(f(x, y, z, t), x), z))*delta*f(x, y, z, t)^5-5*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5-120*(diff(f(x, y, z, t), x))^6+30*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2-(diff(f(x, y, z, t), x))^2*alpha*f(x, y, z, t)^4-f(x, y, z, t)^4*(beta*(diff(f(x, y, z, t), y))+(diff(f(x, y, z, t), z))*delta+9*(diff(f(x, y, z, t), t)))*(diff(f(x, y, z, t), x))+5*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4 = 0

 (11)
> 

collect(F1, {alpha, beta, f(x, y, z, t)})

(-f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2+f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x)))*alpha+(-(diff(f(x, y, z, t), y))*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))+f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), y)))*beta+((diff(diff(f(x, y, z, t), x), z))*delta+diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x)-5*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))+9*(diff(diff(f(x, y, z, t), t), x))-5*(diff(diff(f(x, y, z, t), y), y)))*f(x, y, z, t)^5+(-6*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))-15*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))-10*(diff(diff(diff(f(x, y, z, t), x), x), x))^2+5*(diff(f(x, y, z, t), y))*(diff(diff(diff(f(x, y, z, t), x), x), x))+15*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))+15*(diff(diff(f(x, y, z, t), x), y))*(diff(diff(f(x, y, z, t), x), x))-((diff(f(x, y, z, t), z))*delta+9*(diff(f(x, y, z, t), t)))*(diff(f(x, y, z, t), x))+5*(diff(f(x, y, z, t), y))^2)*f(x, y, z, t)^4+(30*(diff(f(x, y, z, t), x))^2*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))-30*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))+120*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))-30*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*(diff(diff(f(x, y, z, t), x), x))+30*(diff(diff(f(x, y, z, t), x), x))^3)*f(x, y, z, t)^3+(-120*(diff(f(x, y, z, t), x))^3*(diff(diff(diff(f(x, y, z, t), x), x), x))+30*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))-270*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2)*f(x, y, z, t)^2+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-120*(diff(f(x, y, z, t), x))^6 = 0

 (12)
> 

NULL
> 

T := f(x, y, z, t) = g(x, y, z, t)^2+h(x, y, z, t)^2+a[11]
> 

T1 := g(x, y, z, t) = t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5]
> 

T2 := h(x, y, z, t) = t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10]
> 

L2 := subs({T1, T2}, T)

f(x, y, z, t) = (t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11]

 (13)
> 

L3 := eval(F1, L2)

30*(2*a[1]^2+2*a[6]^2)^3*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^3-270*(2*a[1]^2+2*a[6]^2)^2*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^2*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^2+(alpha*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5+360*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^4*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])-30*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[2]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[7])*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^3*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])+15*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^4*(2*a[1]*a[2]+2*a[6]*a[7]))*(2*a[1]^2+2*a[6]^2)+(beta*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5-30*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^2*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^3)*(2*a[1]*a[2]+2*a[6]*a[7])+9*(2*a[1]*a[4]+2*a[6]*a[9])*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5+(2*a[1]*a[3]+2*a[6]*a[8])*delta*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5-5*(2*a[2]^2+2*a[7]^2)*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5-120*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^6+30*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^3*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[2]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[7])*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^2-(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^2*alpha*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^4-((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^4*(beta*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[2]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[7])+(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[3]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[8])*delta+18*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[4]+18*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[9])*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])+5*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[2]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[7])^2*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^4 = 0

 (14)
> 

L4 := collect(L3, [x, y, z, t], 'distributed')

Warning,  computation interrupted

  

` `

 (15)

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