4.21.35 \(-a x y'(x)+x^3+y'(x)^3=0\)

ODE
\[ -a x y'(x)+x^3+y'(x)^3=0 \] ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Use new variable

Mathematica ✗
cpu = 599.997 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.053 (sec), leaf count = 231

\[ \left \{ y \left ( x \right ) =\int \!{i \left ( \left ( {\frac {i}{12}}-{\frac {\sqrt {3}}{12}} \right ) \left ( -108\,{x}^{3}+12\,\sqrt {-12\,{a}^{3}{x}^{3}+81\,{x}^{6}} \right ) ^{{\frac {2}{3}}}+a \left ( \sqrt {3}+i \right ) x \right ) {\frac {1}{\sqrt [3]{-108\,{x}^{3}+12\,\sqrt {-12\,{a}^{3}{x}^{3}+81\,{x}^{6}}}}}}\,{\rm d}x+{\it \_C1},y \left ( x \right ) =\int \!{i \left ( \left ( {\frac {i}{12}}+{\frac {\sqrt {3}}{12}} \right ) \left ( -108\,{x}^{3}+12\,\sqrt {-12\,{a}^{3}{x}^{3}+81\,{x}^{6}} \right ) ^{{\frac {2}{3}}}+a \left ( -\sqrt {3}+i \right ) x \right ) {\frac {1}{\sqrt [3]{-108\,{x}^{3}+12\,\sqrt {-12\,{a}^{3}{x}^{3}+81\,{x}^{6}}}}}}\,{\rm d}x+{\it \_C1},y \left ( x \right ) =\int \!{\frac {1}{6} \left ( \left ( -108\,{x}^{3}+12\,\sqrt {-12\,{a}^{3}{x}^{3}+81\,{x}^{6}} \right ) ^{{\frac {2}{3}}}+12\,ax \right ) {\frac {1}{\sqrt [3]{-108\,{x}^{3}+12\,\sqrt {-12\,{a}^{3}{x}^{3}+81\,{x}^{6}}}}}}\,{\rm d}x+{\it \_C1} \right \} \] Mathematica raw input

DSolve[x^3 - a*x*y'[x] + y'[x]^3 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(diff(y(x),x)^3-a*x*diff(y(x),x)+x^3 = 0, y(x),'implicit')

Maple raw output

y(x) = Int(I*((1/12*I-1/12*3^(1/2))*(-108*x^3+12*(-12*a^3*x^3+81*x^6)^(1/2))^(2/
3)+a*(3^(1/2)+I)*x)/(-108*x^3+12*(-12*a^3*x^3+81*x^6)^(1/2))^(1/3),x)+_C1, y(x) 
= Int(I*((1/12*I+1/12*3^(1/2))*(-108*x^3+12*(-12*a^3*x^3+81*x^6)^(1/2))^(2/3)+a*
(-3^(1/2)+I)*x)/(-108*x^3+12*(-12*a^3*x^3+81*x^6)^(1/2))^(1/3),x)+_C1, y(x) = In
t(1/6*((-108*x^3+12*(-12*a^3*x^3+81*x^6)^(1/2))^(2/3)+12*a*x)/(-108*x^3+12*(-12*
a^3*x^3+81*x^6)^(1/2))^(1/3),x)+_C1