ODE
\[ y''(x)=y(x) f'(x)+(f(x)-2 y(x)) y'(x) \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 39.6725 (sec), leaf count = 0 , could not solve
DSolve[Derivative[2][y][x] == y[x]*Derivative[1][f][x] + (f[x] - 2*y[x])*Derivative[1][y][x], y[x], x]
Maple ✓
cpu = 0.227 (sec), leaf count = 47
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =- \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+f \left ( {\it \_a} \right ) {\it \_b} \left ( {\it \_a} \right ) -{\it \_C1} \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[y''[x] == y[x]*f'[x] + (f[x] - 2*y[x])*y'[x],y[x],x]
Mathematica raw output
DSolve[Derivative[2][y][x] == y[x]*Derivative[1][f][x] + (f[x] - 2*y[x])*Derivative[1][y][x], y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x) = (f(x)-2*y(x))*diff(y(x),x)+diff(f(x),x)*y(x), y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_b(_a),[{diff(_b(_a),_a) = -_b(_a)^2+f(_a)*_b(_a)-_C1}, {_a = x, _b(_a) = y(x)}, {x = _a, y(x) = _b(_a)}])