ODE
\[ y''(x)=y(x) f\left (x,\frac {y'(x)}{y(x)}\right ) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 9.80311 (sec), leaf count = 0 , could not solve
DSolve[Derivative[2][y][x] == f[x, Derivative[1][y][x]/y[x]]*y[x], y[x], x]
Maple ✓
cpu = 0.081 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =- \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+f \left ( {\it \_a},{\it \_b} \left ( {\it \_a} \right ) \right ) \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) ={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }} \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[y''[x] == f[x, y'[x]/y[x]]*y[x],y[x],x]
Mathematica raw output
DSolve[Derivative[2][y][x] == f[x, Derivative[1][y][x]/y[x]]*y[x], y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x) = y(x)*f(x,diff(y(x),x)/y(x)), y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(exp(Int(_b(_a),_a)+_C1),[{diff(_b(_a),_a) = -_b(_a)^2+f(_a,_b(_a))}, {_a = x, _b(_a) = diff(y(x),x)/y(x)}, {x = _a, y(x) = exp(Int(_b(_a),_a)+_C1)}])