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