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Question: how to obtain this simpler solution for this ode

Question:how to obtain this simpler solution for this ode

nm 9899 Maple 2024
ode dsolve differential-equations
March 19 2024
0

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?

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interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

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

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

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

5

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

Intat(1/((_a-c)^(1/2)*(_a-b)^(3/4)*(_a-a)^(3/4)), _a = y(x))+Intat(-(-f(_a)*(-y(x)+c)^2*(-y(x)+b)^3*(-y(x)+a)^3)^(1/4)/((y(x)-c)^(1/2)*(y(x)-b)^(3/4)*(y(x)-a)^(3/4)), _a = x)+c__1 = 0

0

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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)

Intat(1/((_a-c)^(2/3)*(_a-b)*(_a-a))^(3/4), _a = y(x)) = Intat((-f(_a))^(1/4), _a = x)+c__1

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Download why_not_this_simpler_solution.mw

Hand solution

Maple 2024
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