4.18.10 $-x^2+x{y}^{\prime }(x{)}^2+y(x)y^{\prime }(x)=0$

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

[[_homogeneous, `class G`], _rational]

Book solution method
Homogeneous ODE, The Isobaric equation

Mathematica ✗
cpu = 600.002 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.178 (sec), leaf count = 269

$$\{{\int }_{\mathit{\_}\mathit{b}}^x\frac{1}{\mathit{\_}\mathit{a}}(-y\left(x\right)-\sqrt{4{\mathit{\_}\mathit{a}}^3+{\left(y\left(x\right)\right)}^2}){(\sqrt{4{\mathit{\_}\mathit{a}}^3+{\left(y\left(x\right)\right)}^2}+4y\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}1(-2+(-48\mathit{\_}\mathit{f}-12\sqrt{4x^3+{\mathit{\_}\mathit{f}}^2}){\int }_{\mathit{\_}\mathit{b}}^x{\mathit{\_}\mathit{a}}^2{(\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2}+4\mathit{\_}\mathit{f})}^{-2}\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}){(\sqrt{4x^3+{\mathit{\_}\mathit{f}}^2}+4\mathit{\_}\mathit{f})}^{-1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0,{\int }_{\mathit{\_}\mathit{b}}^x\frac{1}{\mathit{\_}\mathit{a}}(-y\left(x\right)+\sqrt{4{\mathit{\_}\mathit{a}}^3+{\left(y\left(x\right)\right)}^2}){(4y\left(x\right)-\sqrt{4{\mathit{\_}\mathit{a}}^3+{\left(y\left(x\right)\right)}^2})}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}1(-2+(48\mathit{\_}\mathit{f}-12\sqrt{4x^3+{\mathit{\_}\mathit{f}}^2}){\int }_{\mathit{\_}\mathit{b}}^x{\mathit{\_}\mathit{a}}^2{(-4\mathit{\_}\mathit{f}+\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2})}^{-2}\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{f}}^2}}\mathrm{d}\mathit{\_}\mathit{a}){(4\mathit{\_}\mathit{f}-\sqrt{4x^3+{\mathit{\_}\mathit{f}}^2})}^{-1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[-x^2 + y[x]*y'[x] + x*y'[x]^2 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(x*diff(y(x),x)^2+y(x)*diff(y(x),x)-x^2 = 0, y(x),'implicit')

Maple raw output

Int((-y(x)+(4*_a^3+y(x)^2)^(1/2))/(4*y(x)-(4*_a^3+y(x)^2)^(1/2))/_a,_a = _b .. x
)+Intat((-2+(48*_f-12*(4*x^3+_f^2)^(1/2))*Int(1/(-4*_f+(4*_a^3+_f^2)^(1/2))^2*_a
^2/(4*_a^3+_f^2)^(1/2),_a = _b .. x))/(4*_f-(4*x^3+_f^2)^(1/2)),_f = y(x))+_C1 =
 0, Int((-y(x)-(4*_a^3+y(x)^2)^(1/2))/((4*_a^3+y(x)^2)^(1/2)+4*y(x))/_a,_a = _b 
.. x)+Intat((-2+(-48*_f-12*(4*x^3+_f^2)^(1/2))*Int(1/((4*_a^3+_f^2)^(1/2)+4*_f)^
2*_a^2/(4*_a^3+_f^2)^(1/2),_a = _b .. x))/((4*x^3+_f^2)^(1/2)+4*_f),_f = y(x))+_
C1 = 0