ODE
\[ f(x) f'(x) y'(x)+f(x)^2 y''(x)=g\left (y(x),f(x) y'(x)\right ) \] ODE Classification
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Book solution method
TO DO
Mathematica ✗
cpu = 1.05969 (sec), leaf count = 0 , could not solve
DSolve[f[x]*Derivative[1][f][x]*Derivative[1][y][x] + f[x]^2*Derivative[2][y][x] == g[y[x], f[x]*Derivative[1][y][x]], y[x], x]
Maple ✗
cpu = 0.666 (sec), leaf count = 0 , result contains DESol or ODESolStruc
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Mathematica raw input
DSolve[f[x]*f'[x]*y'[x] + f[x]^2*y''[x] == g[y[x], f[x]*y'[x]],y[x],x]
Mathematica raw output
DSolve[f[x]*Derivative[1][f][x]*Derivative[1][y][x] + f[x]^2*Derivative[2][y][x] == g[y[x], f[x]*Derivative[1][y][x]], y[x], x]
Maple raw input
dsolve(f(x)^2*diff(diff(y(x),x),x)+f(x)*diff(f(x),x)*diff(y(x),x) = g(y(x),f(x)*diff(y(x),x)), y(x))
Maple raw output
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