ODE
\[ y'(x) f\left (\frac {y''(x)}{y'(x)}\right )=y'(x)^2-y(x) y''(x) \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.160676 (sec), leaf count = 0 , could not solve
DSolve[f[Derivative[2][y][x]/Derivative[1][y][x]]*Derivative[1][y][x] == Derivative[1][y][x]^2 - y[x]*Derivative[2][y][x], y[x], x]
Maple ✓
cpu = 2.505 (sec), leaf count = 13
\[[y \left (x \right ) = {\mathrm e}^{\textit {\_C2} \textit {\_C1}} {\mathrm e}^{\textit {\_C1} x}]\] Mathematica raw input
DSolve[f[y''[x]/y'[x]]*y'[x] == y'[x]^2 - y[x]*y''[x],y[x],x]
Mathematica raw output
DSolve[f[Derivative[2][y][x]/Derivative[1][y][x]]*Derivative[1][y][x] == Derivative[1][y][x]^2 - y[x]*Derivative[2][y][x], y[x], x]
Maple raw input
dsolve(diff(y(x),x)*f(diff(diff(y(x),x),x)/diff(y(x),x)) = diff(y(x),x)^2-y(x)*diff(diff(y(x),x),x), y(x))
Maple raw output
[y(x) = exp(_C2*_C1)*exp(_C1*x)]