ODE
\[ x^2 y''(x)=y(x) f\left (\frac {x y'(x)}{y(x)}\right ) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 419.83 (sec), leaf count = 0 , could not solve
DSolve[x^2*Derivative[2][y][x] == f[(x*Derivative[1][y][x])/y[x]]*y[x], y[x], x]
Maple ✓
cpu = 0.048 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={{\rm e}^{\int ^{\ln \left ( x \right ) }\!{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( {\it \_a}-{{\it \_a}}^{2}+f \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}-{\it \_b}+{\it \_C1} \right ) {d{\it \_b}}+{\it \_C2}}} \right \} \] Mathematica raw input
DSolve[x^2*y''[x] == f[(x*y'[x])/y[x]]*y[x],y[x],x]
Mathematica raw output
DSolve[x^2*Derivative[2][y][x] == f[(x*Derivative[1][y][x])/y[x]]*y[x], y[x], x]
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x) = y(x)*f(x*diff(y(x),x)/y(x)), y(x),'implicit')
Maple raw output
y(x) = exp(Intat(RootOf(Intat(1/(_a-_a^2+f(_a)),_a = _Z)-_b+_C1),_b = ln(x))+_C2)