# Question:why Maple gives all those extra solutions for this ode?

## Question:why Maple gives all those extra solutions for this ode?

Maple 2019

This ODE turns out to be a simple separable ODE. With one solution, if the ODE is rewritten.

But in its original form, Maple dsolve gives 6 complicated looking solutions with complex numbers in some of them. Even though all 6 solutions are valid.

Any one knows why Maple did that and not give the one simple solution instead?

I used isolate to solve for y' from the original ODE. Verfiied that only one solution exist.  The ODE then became y'(x)= 3*y(x)/(2*x). Which by uniqueness theorem, should have one unique solution in some region in the RHS or in some region in the LHS that does not inculde x=0 ?

Just wondering what is going on, and why Maple did not give same simpler solution, so I can learn something new. That is all.

 > restart;
 > Typesetting:-Settings(typesetprime=true):
 > ode:= 1/2*(2*x^(5/2)-3*y(x)^(5/3))/x^(5/2)/y(x)^(2/3)+1/3*(-2*x^(5/2)+3*y(x)^(5/3))*diff(y(x),x)/x^(3/2)/y(x)^(5/3) = 0;

 > maple_sol:=dsolve(ode);

 > map(x->odetest(x,ode),[maple_sol])

 > solve(ode,diff(y(x),x),AllSolutions)

 > ode2:=isolate(ode,diff(y(x),x)); #solve for y' first

 > ode2:=simplify(ode2)

 > sol:=dsolve(ode2)

 > odetest(sol,ode2)

Maple 2019.1

Physics 395

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