ODE
\[ \left (x^2+2 y(x)^2 y'(x)\right ) y''(x)+2 y(x) y'(x)^3+3 x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✗
cpu = 42.367 (sec), leaf count = 0 , could not solve
DSolve[y[x] + 3*x*Derivative[1][y][x] + 2*y[x]*Derivative[1][y][x]^3 + (x^2 + 2*y[x]^2*Derivative[1][y][x])*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 2.223 (sec), leaf count = 54
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{{\it \_a}}^{2}{\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) +{\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +{\it \_C1}=0 \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[y[x] + 3*x*y'[x] + 2*y[x]*y'[x]^3 + (x^2 + 2*y[x]^2*y'[x])*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[y[x] + 3*x*Derivative[1][y][x] + 2*y[x]*Derivative[1][y][x]^3 + (x^2 + 2*y[x]^2*Derivative[1][y][x])*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve((x^2+2*y(x)^2*diff(y(x),x))*diff(diff(y(x),x),x)+2*y(x)*diff(y(x),x)^3+3*x*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_b(_a),[{_b(_a)^2*diff(_b(_a),_a)^2+_a^2*diff(_b(_a),_a)+_a*_b(_a)+_C1 = 0}, {_a = x, _b(_a) = y(x)}, {x = _a, y(x) = _b(_a)}])