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Question: How find conditions by comparing two equations?

Question:How find conditions by comparing two equations?

Math-dashti 135 Maple 2024
ode homework differential-equations
June 28 2025
1

in a lot of equation i have this problem which they find a condition by comparing  the  equation regarding to term must have 3 condition but i don't know why he found just one condition how we can get condition from E8&E9


 

> 

restart
> 

with(PDEtools)
> 

undeclare(prime, quiet)
> 

with(LinearAlgebra)
> 

declare(u(x, y, t), quiet); declare(U(xi), quiet); declare(V(xi), quiet); declare(W(x, y, t), quiet); declare(V(x, y, t), quiet)
> 

E9 := 2*k[2]*U(xi)^3+(-2*k[1]*p[1]*p[2]-k[2]*p[1]^2+k[3])*U(xi)+k[1]^2*k[2]*(diff(diff(U(xi), xi), xi)) = 0

2*k[2]*U(xi)^3+(-2*k[1]*p[1]*p[2]-k[2]*p[1]^2+k[3])*U(xi)+k[1]^2*k[2]*(diff(diff(U(xi), xi), xi)) = 0

 (1)
> 

E8 := (2*k[1]*p[2]+4*k[2]*p[1])*U(xi)^3+(-k[1]*p[1]^2*p[2]+k[1]*p[3])*U(xi)+(k[1]^3*p[2]+2*k[1]^2*k[2]*p[1])*(diff(diff(U(xi), xi), xi)) = 0

(2*k[1]*p[2]+4*k[2]*p[1])*U(xi)^3+(-k[1]*p[1]^2*p[2]+k[1]*p[3])*U(xi)+(k[1]^3*p[2]+2*k[1]^2*k[2]*p[1])*(diff(diff(U(xi), xi), xi)) = 0

 (2)
 

NULL

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