4.37.41 \(y''(x)=y(x) f\left (x,\frac {y'(x)}{y(x)}\right )\)

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 = 8.14979 (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 = 0.224 (sec), leaf count = 0 , result contains DESol or ODESolStruc

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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))

Maple raw output

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