ODE
\[ \left (2 x^2 y'(x)+y(x)^2\right ) y''(x)+2 (y(x)+x) y'(x)^2+x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✗
cpu = 42.0799 (sec), leaf count = 0 , could not solve
DSolve[y[x] + x*Derivative[1][y][x] + 2*(x + y[x])*Derivative[1][y][x]^2 + (y[x]^2 + 2*x^2*Derivative[1][y][x])*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 1.422 (sec), leaf count = 54
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ {{\it \_a}}^{2} \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+ \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}{\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) +{\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +{\it \_C1}=0 \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[y[x] + x*y'[x] + 2*(x + y[x])*y'[x]^2 + (y[x]^2 + 2*x^2*y'[x])*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[y[x] + x*Derivative[1][y][x] + 2*(x + y[x])*Derivative[1][y][x]^2 + (y[x]^2 + 2*x^2*Derivative[1][y][x])*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve((y(x)^2+2*x^2*diff(y(x),x))*diff(diff(y(x),x),x)+2*(x+y(x))*diff(y(x),x)^2+x*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_b(_a),[{_a^2*diff(_b(_a),_a)^2+_b(_a)^2*diff(_b(_a),_a)+_a*_b(_a)+_C1 = 0}, {_a = x, _b(_a) = y(x)}, {x = _a, y(x) = _b(_a)}])