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 = 0.2052 (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 = 0.291 (sec), leaf count = 34
\[\left [y \left (x \right ) = \frac {\int \textit {\_C1} \,{\mathrm e}^{\int f \left (x \right )d x}d x +\textit {\_C2}}{\int \int \textit {\_C1} \,{\mathrm e}^{\int f \left (x \right )d x}d x d x +\textit {\_C2} x +1}\right ]\] 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))
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)]