4.21.5 $(a-x^3-y(x{)}^3)y^{\prime }(x)+x^{2}y(x)+xy(x{)}^2{y}^{\prime }(x{)}^2=0$

ODE
$$(a-x^3-y(x{)}^3)y^{\prime }(x)+x^{2}y(x)+xy(x{)}^2{y}^{\prime }(x{)}^2=0$$ 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

$$\{{\left(y\left(x\right)\right)}^6+(-2x^3-2a){\left(y\left(x\right)\right)}^3+{(-x^3+a)}^2=0,{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt{x^6+(-2{\mathit{\_}\mathit{a}}^3-2a)x^3+{(-{\mathit{\_}\mathit{a}}^3+a)}^2}}\mathrm{d}\mathit{\_}\mathit{a}-\frac{\ln \left(x\right)}{2}-\mathit{\_}\mathit{C}\mathit{1}=0,{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt{x^6+(-2{\mathit{\_}\mathit{a}}^3-2a)x^3+{(-{\mathit{\_}\mathit{a}}^3+a)}^2}}\mathrm{d}\mathit{\_}\mathit{a}+\frac{\ln \left(x\right)}{2}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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