ODE
\[ y''(x)=(f(x)-3 y(x)) y'(x)+f(x) y(x)^2-y(x)^3 \] ODE Classification
[[_2nd_order, _with_potential_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.0389145 (sec), leaf count = 0 , could not solve
DSolve[Derivative[2][y][x] == f[x]*y[x]^2 - y[x]^3 + (f[x] - 3*y[x])*Derivative[1][y][x], y[x], x]
Maple ✓
cpu = 0.07 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) +{\frac {-\int \!{\it \_C1}\,{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x-{\it \_C2}}{\int \!\!\!\int \!{\it \_C1}\,{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x\,{\rm d}x+{\it \_C2}\,x+1}}=0 \right \} \] Mathematica raw input
DSolve[y''[x] == f[x]*y[x]^2 - y[x]^3 + (f[x] - 3*y[x])*y'[x],y[x],x]
Mathematica raw output
DSolve[Derivative[2][y][x] == f[x]*y[x]^2 - y[x]^3 + (f[x] - 3*y[x])*Derivative[1][y][x], y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x) = (f(x)-3*y(x))*diff(y(x),x)+f(x)*y(x)^2-y(x)^3, y(x),'implicit')
Maple raw output
y(x)+(-Int(_C1*exp(Int(f(x),x)),x)-_C2)/(Int(Int(_C1*exp(Int(f(x),x)),x),x)+_C2*x+1) = 0