4.18.11 \(x^3+x y'(x)^2+y(x) y'(x)=0\)

ODE
\[ x^3+x y'(x)^2+y(x) y'(x)=0 \] ODE Classification

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

Book solution method
Homogeneous ODE, The Isobaric equation

Mathematica
cpu = 600.003 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.183 (sec), leaf count = 269

\[ \left \{ \int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left (-y \relax (x ) -\sqrt {-4\,{{\it \_a}}^{4}+ \left (y \relax (x ) \right ) ^{2}} \right ) \left (\sqrt {-4\,{{\it \_a}}^{4}+ \left (y \relax (x ) \right ) ^{2}}+5\,y \relax (x ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \relax (x ) }\!{1 \left (-2+ \left (80\,{\it \_f}+16\,\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}} \right ) \int _{{\it \_b}}^{x}\!{{{\it \_a}}^{3} \left (\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f} \right ) ^{-2}{\frac {1}{\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}}\,{\rm d}{\it \_a} \right ) \left (\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left (-y \relax (x ) +\sqrt {-4\,{{\it \_a}}^{4}+ \left (y \relax (x ) \right ) ^{2}} \right ) \left (5\,y \relax (x ) -\sqrt {-4\,{{\it \_a}}^{4}+ \left (y \relax (x ) \right ) ^{2}} \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \relax (x ) }\!{1 \left (-2+ \left (-80\,{\it \_f}+16\,\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}} \right ) \int _{{\it \_b}}^{x}\!{{{\it \_a}}^{3} \left (-5\,{\it \_f}+\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}} \right ) ^{-2}{\frac {1}{\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}}\,{\rm d}{\it \_a} \right ) \left (5\,{\it \_f}-\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[x^3 + 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^3 = 0, y(x),'implicit')

Maple raw output

Int((-y(x)+(-4*_a^4+y(x)^2)^(1/2))/(5*y(x)-(-4*_a^4+y(x)^2)^(1/2))/_a,_a = _b ..
 x)+Intat((-2+(-80*_f+16*(-4*x^4+_f^2)^(1/2))*Int(1/(-5*_f+(-4*_a^4+_f^2)^(1/2))
^2*_a^3/(-4*_a^4+_f^2)^(1/2),_a = _b .. x))/(5*_f-(-4*x^4+_f^2)^(1/2)),_f = y(x)
)+_C1 = 0, Int((-y(x)-(-4*_a^4+y(x)^2)^(1/2))/((-4*_a^4+y(x)^2)^(1/2)+5*y(x))/_a
,_a = _b .. x)+Intat((-2+(80*_f+16*(-4*x^4+_f^2)^(1/2))*Int(1/((-4*_a^4+_f^2)^(1
/2)+5*_f)^2*_a^3/(-4*_a^4+_f^2)^(1/2),_a = _b .. x))/((-4*x^4+_f^2)^(1/2)+5*_f),
_f = y(x))+_C1 = 0