ODE
\[ a x+y(x)^2 y''(x)+y(x) y'(x)^2=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 4.06422 (sec), leaf count = 0 , could not solve
DSolve[a*x + y[x]*Derivative[1][y][x]^2 + y[x]^2*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 1.274 (sec), leaf count = 112
\[ \left \{ \ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {{{\it \_g}}^{2}}{2\,{{\it \_g}}^{3}+2\,a} \left ( \sqrt [3]{{\frac {a}{{{\it \_g}}^{3}}}}\sqrt {3}\tan \left ( {\it RootOf} \left ( -2\,{\it \_Z}\,\sqrt {3}+\ln \left ( {\frac { \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1}{3+2\,\sqrt {3}\tan \left ( {\it \_Z} \right ) + \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +6\,{\it \_C1}+6\,\int \!{\frac {{{\it \_g}}^{2}}{{{\it \_g}}^{3}+a} \left ( {\frac {a}{{{\it \_g}}^{3}}} \right ) ^{2/3}}\,{\rm d}{\it \_g} \right ) \right ) +\sqrt [3]{{\frac {a}{{{\it \_g}}^{3}}}}-2 \right ) }{d{\it \_g}}-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[a*x + y[x]*y'[x]^2 + y[x]^2*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[a*x + y[x]*Derivative[1][y][x]^2 + y[x]^2*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(y(x)^2*diff(diff(y(x),x),x)+y(x)*diff(y(x),x)^2+a*x = 0, y(x),'implicit')
Maple raw output
ln(x)-Intat(_g^2*((1/_g^3*a)^(1/3)*3^(1/2)*tan(RootOf(-2*_Z*3^(1/2)+ln((tan(_Z)^2+1)/(3+2*3^(1/2)*tan(_Z)+tan(_Z)^2))+6*_C1+6*Int((1/_g^3*a)^(2/3)/(_g^3+a)*_g^2,_g)))+(1/_g^3*a)^(1/3)-2)/(2*_g^3+2*a),_g = y(x)/x)-_C2 = 0