ODE
\[ y'(x) y''(x)=x^2 y(x) y'(x)+x y(x)^2 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✗
cpu = 61.5678 (sec), leaf count = 0 , could not solve
DSolve[Derivative[1][y][x]*Derivative[2][y][x] == x*y[x]^2 + x^2*y[x]*Derivative[1][y][x], y[x], x]
Maple ✓
cpu = 1.967 (sec), leaf count = 46
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ -{{\it \_a}}^{2} \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{\it \_C1}=0 \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[y'[x]*y''[x] == x*y[x]^2 + x^2*y[x]*y'[x],y[x],x]
Mathematica raw output
DSolve[Derivative[1][y][x]*Derivative[2][y][x] == x*y[x]^2 + x^2*y[x]*Derivative[1][y][x], y[x], x]
Maple raw input
dsolve(diff(y(x),x)*diff(diff(y(x),x),x) = x^2*y(x)*diff(y(x),x)+x*y(x)^2, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_b(_a),[{-_a^2*_b(_a)^2+diff(_b(_a),_a)^2+_C1 = 0}, {_a = x, _b(_a) = y(x)}, {x = _a, y(x) = _b(_a)}])