# Question:how to obtain this simpler solution for this ode

## Question:how to obtain this simpler solution for this ode

Maple 2024

I was wondering why Maple do not give this simpler solution to this ode. It solves it as exact. But if solved as separable, the solution is much simpler.

I solved this by hand and Maple verifies my solution. You can see the separable solution is much simpler. Any tricks to make Maple gives the simpler solution?

 > interface(version);

 > ode:=diff(y(x),x)^4+f(x)*(y(x)-a)^3*(y(x)-b)^3*(y(x)-c)^2 = 0;

 > infolevel[dsolve]:=5; sol:=dsolve(ode); odetest(sol,ode);

Methods for first order ODEs:

-> Solving 1st order ODE of high degree, 1st attempt

trying 1st order WeierstrassP solution for high degree ODE

trying 1st order WeierstrassPPrime solution for high degree ODE

trying 1st order JacobiSN solution for high degree ODE

trying 1st order ODE linearizable_by_differentiation

trying differential order: 1; missing variables

trying simple symmetries for implicit equations

--- Trying classification methods ---

trying homogeneous types:

trying exact

<- exact successful

 > mysol:=Intat(1/( (_a-c)^(2/3)*(_a-b)*(_a-a))^(3/4),_a = y(x))=Intat( (-f(_a))^(1/4),_a=x)+_C1; odetest(mysol,ode)