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 = 0.0126855 (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 = 0.259 (sec), leaf count = 17
\[ \left \{ {\frac {\ln \left ( y \left ( x \right ) \right ) }{{\it \_C1}}}-x-{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
1/_C1*ln(y(x))-x-_C2 = 0