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Question: how to make odetest() verify dsolve solution on this ODE

Question:how to make odetest() verify dsolve solution on this ODE

nm 8552 Maple 2019
differential-equations odetest
July 26 2019
1

THis is another ode which I am not able to get odetest to give zero. Any one knows of a trick to verify this solution? It might be just that the solution is too complicated for odetest to verify?


 

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restart;
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ode:=diff(y(x),x)*(x^3+1)^(2/3)+(1+y(x)^3)^(2/3) = 0;
sol:=dsolve(ode);

(diff(y(x), x))*(x^3+1)^(2/3)+(1+y(x)^3)^(2/3) = 0

x*hypergeom([1/3, 2/3], [4/3], -x^3)+y(x)*hypergeom([1/3, 2/3], [4/3], -y(x)^3)+_C1 = 0

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odetest(sol,ode);

-9*(1+y(x)^3)^(1/3)*(x^3+1)^(2/3)*hypergeom([4/3, 5/3], [7/3], -x^3)*x^3*GAMMA(2/3)*(-y(x)^3)^(1/6)/(9*hypergeom([4/3, 5/3], [7/3], -y(x)^3)*y(x)^3*(-y(x)^3)^(1/6)*(1+y(x)^3)^(1/3)*GAMMA(2/3)-4*Pi*3^(1/2)*LegendreP(-1/3, -1/3, -y(x)^3/(1+y(x)^3)+1/(1+y(x)^3)))+9*y(x)^6*hypergeom([4/3, 5/3], [7/3], -y(x)^3)*GAMMA(2/3)*(-y(x)^3)^(1/6)/(9*hypergeom([4/3, 5/3], [7/3], -y(x)^3)*y(x)^3*(-y(x)^3)^(1/6)*(1+y(x)^3)^(1/3)*GAMMA(2/3)-4*Pi*3^(1/2)*LegendreP(-1/3, -1/3, -y(x)^3/(1+y(x)^3)+1/(1+y(x)^3)))+9*y(x)^3*hypergeom([4/3, 5/3], [7/3], -y(x)^3)*GAMMA(2/3)*(-y(x)^3)^(1/6)/(9*hypergeom([4/3, 5/3], [7/3], -y(x)^3)*y(x)^3*(-y(x)^3)^(1/6)*(1+y(x)^3)^(1/3)*GAMMA(2/3)-4*Pi*3^(1/2)*LegendreP(-1/3, -1/3, -y(x)^3/(1+y(x)^3)+1/(1+y(x)^3)))-4*(1+y(x)^3)^(2/3)*Pi*3^(1/2)*LegendreP(-1/3, -1/3, -(y(x)^3-1)/(1+y(x)^3))/(9*hypergeom([4/3, 5/3], [7/3], -y(x)^3)*y(x)^3*(-y(x)^3)^(1/6)*(1+y(x)^3)^(1/3)*GAMMA(2/3)-4*Pi*3^(1/2)*LegendreP(-1/3, -1/3, -y(x)^3/(1+y(x)^3)+1/(1+y(x)^3)))+4*(1+y(x)^3)^(1/3)*(x^3+1)^(1/3)*Pi*3^(1/2)*LegendreP(-1/3, -1/3, -(x^3-1)/(x^3+1))*(-y(x)^3)^(1/6)/((-x^3)^(1/6)*(9*hypergeom([4/3, 5/3], [7/3], -y(x)^3)*y(x)^3*(-y(x)^3)^(1/6)*(1+y(x)^3)^(1/3)*GAMMA(2/3)-4*Pi*3^(1/2)*LegendreP(-1/3, -1/3, -y(x)^3/(1+y(x)^3)+1/(1+y(x)^3))))

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simplify(%);

-9*((4/9)*(1+y(x)^3)^(2/3)*Pi*3^(1/2)*LegendreP(-1/3, -1/3, (-y(x)^3+1)/(1+y(x)^3))*(-x^3)^(1/6)+(-(4/9)*(1+y(x)^3)^(1/3)*(x^3+1)^(1/3)*Pi*3^(1/2)*LegendreP(-1/3, -1/3, (-x^3+1)/(x^3+1))+(-x^3)^(1/6)*((-y(x)^6-y(x)^3)*hypergeom([4/3, 5/3], [7/3], -y(x)^3)+x^3*(1+y(x)^3)^(1/3)*hypergeom([4/3, 5/3], [7/3], -x^3)*(x^3+1)^(2/3))*GAMMA(2/3))*(-y(x)^3)^(1/6))/((-x^3)^(1/6)*(9*hypergeom([4/3, 5/3], [7/3], -y(x)^3)*y(x)^3*(-y(x)^3)^(1/6)*(1+y(x)^3)^(1/3)*GAMMA(2/3)-4*Pi*3^(1/2)*LegendreP(-1/3, -1/3, (-y(x)^3+1)/(1+y(x)^3))))

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