ODE
\[ y(x) y''(x)=-y(x) \left (f'(x)-y(x)^2 g'(x)\right )+y'(x) \left (f(x)+g(x) y(x)^2\right )+y'(x)^2 \] ODE Classification
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Book solution method
TO DO
Mathematica ✗
cpu = 21.1292 (sec), leaf count = 0 , could not solve
DSolve[y[x]*Derivative[2][y][x] == -(y[x]*(Derivative[1][f][x] - y[x]^2*Derivative[1][g][x])) + (f[x] + g[x]*y[x]^2)*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 1.069 (sec), leaf count = 0 , result contains DESol or ODESolStruc
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Mathematica raw input
DSolve[y[x]*y''[x] == -(y[x]*(f'[x] - y[x]^2*g'[x])) + (f[x] + g[x]*y[x]^2)*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
DSolve[y[x]*Derivative[2][y][x] == -(y[x]*(Derivative[1][f][x] - y[x]^2*Derivative[1][g][x])) + (f[x] + g[x]*y[x]^2)*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+(f(x)+g(x)*y(x)^2)*diff(y(x),x)-y(x)*(diff(f(x),x)-diff(g(x),x)*y(x)^2), y(x))
Maple raw output
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