ODE
\[ y(x) y''(x)=a y(x) y'(x)+b y(x)^2+y'(x)^2+y(x)^3 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 47.8136 (sec), leaf count = 0 , could not solve
DSolve[y[x]*Derivative[2][y][x] == b*y[x]^2 + y[x]^3 + a*y[x]*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple ✓
cpu = 1.509 (sec), leaf count = 68
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) -{\frac { \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+a{\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +b{{\it \_a}}^{2}+{{\it \_a}}^{3}}{{\it \_a}}}=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[y[x]*y''[x] == b*y[x]^2 + y[x]^3 + a*y[x]*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
DSolve[y[x]*Derivative[2][y][x] == b*y[x]^2 + y[x]^3 + a*y[x]*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+a*y(x)*diff(y(x),x)+b*y(x)^2+y(x)^3, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a,[{diff(_b(_a),_a)*_b(_a)-(_b(_a)^2+a*_a*_b(_a)+b*_a^2+_a^3)/_a = 0}, {_a = y(x), _b(_a) = diff(y(x),x)}, {x = Int(1/_b(_a),_a)+_C1, y(x) = _a}])