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 = 1.72579 (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 = 0.236 (sec), leaf count = 33
\[\left [y \left (x \right ) = {\mathrm e}^{\int _{}^{\ln \left (x \right )}\RootOf \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} -\textit {\_a}^{2}+f \left (\textit {\_a} \right )}d \textit {\_a} -\textit {\_b} +\textit {\_C1} \right )d \textit {\_b} +\textit {\_C2}}\right ]\] 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))
Maple raw output
[y(x) = exp(Intat(RootOf(Intat(1/(_a-_a^2+f(_a)),_a = _Z)-_b+_C1),_b = ln(x))+_C2)]