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

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

nm 8552 Maple 2019
ode dsolve differential-equations
August 09 2019
0

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.

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restart;
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Typesetting:-Settings(typesetprime=true):
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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;

(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

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DEtools:-odeadvisor(ode);

[[_1st_order, _with_linear_symmetries], _exact, _rational]

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maple_sol:=dsolve(ode);

y(x) = (1/3)*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), y(x) = (1/3)*(-(1/4)*5^(1/2)-1/4-((1/4)*I)*2^(1/2)*(5-5^(1/2))^(1/2))^3*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), y(x) = (1/3)*(-(1/4)*5^(1/2)-1/4+((1/4)*I)*2^(1/2)*(5-5^(1/2))^(1/2))^3*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), y(x) = (1/3)*((1/4)*5^(1/2)-1/4-((1/4)*I)*2^(1/2)*(5+5^(1/2))^(1/2))^3*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), y(x) = (1/3)*((1/4)*5^(1/2)-1/4+((1/4)*I)*2^(1/2)*(5+5^(1/2))^(1/2))^3*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), x/y(x)^(2/3)+y(x)/x^(3/2)+_C1 = 0

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

[0, 0, 0, 0, 0, 0]

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

(3/2)*y(x)/x

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

diff(y(x), x) = -(3/2)*(2*x^(5/2)-3*y(x)^(5/3))*y(x)/(x*(-2*x^(5/2)+3*y(x)^(5/3)))

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ode2:=simplify(ode2)

diff(y(x), x) = (3/2)*y(x)/x

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DEtools:-odeadvisor(ode2);

[_separable]

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sol:=dsolve(ode2)

y(x) = _C1*x^(3/2)

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odetest(sol,ode2)

0

 

Download strange_ode_answer.mw

Maple 2019.1

Physics 395
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