ODE
\[ f(y(x)) y''(x)=f(y(x))^2 \text {F0}\left (x,\frac {y'(x)}{f(y(x))}\right )+y'(x)^2 f'(y(x)) \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 2.72382 (sec), leaf count = 0 , could not solve
DSolve[f[y[x]]*Derivative[2][y][x] == f[y[x]]^2*F0[x, Derivative[1][y][x]/f[y[x]]] + Derivative[1][f][y[x]]*Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 0.059 (sec), leaf count = 0 , exception
unable to handle composite functions containing y(x) or diff(y(x),x) as in eval(diff(f(u),u),{u = y(x)})
Mathematica raw input
DSolve[f[y[x]]*y''[x] == f[y[x]]^2*F0[x, y'[x]/f[y[x]]] + f'[y[x]]*y'[x]^2,y[x],x]
Mathematica raw output
DSolve[f[y[x]]*Derivative[2][y][x] == f[y[x]]^2*F0[x, Derivative[1][y][x]/f[y[x]]] + Derivative[1][f][y[x]]*Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(f(y(x))*diff(diff(y(x),x),x) = eval(diff(f(u),u),{u = y(x)})*diff(y(x),x)^2+f(y(x))^2*F0(x,diff(y(x),x)/f(y(x))), y(x),'implicit')
Maple raw output
unable to handle composite functions containing y(x) or diff(y(x),x) as in eval(diff(f(u),u),{u = y(x)})