ODE
\[ \left (a-x^3-y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0 \] ODE Classification
[_rational]
Book solution method
Change of variable
Mathematica ✗
cpu = 599.998 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 1.357 (sec), leaf count = 129
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{6}+ \left ( -2\,{x}^{3}-2\,a \right ) \left ( y \left ( x \right ) \right ) ^{3}+ \left ( -{x}^{3}+a \right ) ^{2}=0,\int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {{x}^{6}+ \left ( -2\,{{\it \_a}}^{3}-2\,a \right ) {x}^{3}+ \left ( -{{\it \_a}}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}-{\frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0,\int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {{x}^{6}+ \left ( -2\,{{\it \_a}}^{3}-2\,a \right ) {x}^{3}+ \left ( -{{\it \_a}}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}+{\frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x^2*y[x] + (a - x^3 - y[x]^3)*y'[x] + x*y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x*y(x)^2*diff(y(x),x)^2+(a-x^3-y(x)^3)*diff(y(x),x)+x^2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x)^6+(-2*x^3-2*a)*y(x)^3+(-x^3+a)^2 = 0, Int(1/(x^6+(-2*_a^3-2*a)*x^3+(-_a^3+a)^2)^(1/2)*_a^2,_a = _b .. y(x))+1/2*ln(x)-_C1 = 0, Int(1/(x^6+(-2*_a^3-2*a)*x^3+(-_a^3+a)^2)^(1/2)*_a^2,_a = _b .. y(x))-1/2*ln(x)-_C1 = 0