4.18.10 \(-x^2+x y'(x)^2+y(x) y'(x)=0\)

ODE
\[ -x^2+x y'(x)^2+y(x) y'(x)=0 \] 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

\[ \left \{ \int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left (-y \relax (x ) -\sqrt {4\,{{\it \_a}}^{3}+ \left (y \relax (x ) \right ) ^{2}} \right ) \left (\sqrt {4\,{{\it \_a}}^{3}+ \left (y \relax (x ) \right ) ^{2}}+4\,y \relax (x ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \relax (x ) }\!{1 \left (-2+ \left (-48\,{\it \_f}-12\,\sqrt {4\,{x}^{3}+{{\it \_f}}^{2}} \right ) \int _{{\it \_b}}^{x}\!{{{\it \_a}}^{2} \left (\sqrt {4\,{{\it \_a}}^{3}+{{\it \_f}}^{2}}+4\,{\it \_f} \right ) ^{-2}{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{{\it \_f}}^{2}}}}}\,{\rm d}{\it \_a} \right ) \left (\sqrt {4\,{x}^{3}+{{\it \_f}}^{2}}+4\,{\it \_f} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left (-y \relax (x ) +\sqrt {4\,{{\it \_a}}^{3}+ \left (y \relax (x ) \right ) ^{2}} \right ) \left (4\,y \relax (x ) -\sqrt {4\,{{\it \_a}}^{3}+ \left (y \relax (x ) \right ) ^{2}} \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \relax (x ) }\!{1 \left (-2+ \left (48\,{\it \_f}-12\,\sqrt {4\,{x}^{3}+{{\it \_f}}^{2}} \right ) \int _{{\it \_b}}^{x}\!{{{\it \_a}}^{2} \left (-4\,{\it \_f}+\sqrt {4\,{{\it \_a}}^{3}+{{\it \_f}}^{2}} \right ) ^{-2}{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{{\it \_f}}^{2}}}}}\,{\rm d}{\it \_a} \right ) \left (4\,{\it \_f}-\sqrt {4\,{x}^{3}+{{\it \_f}}^{2}} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0 \right \} \] 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