ODE
\[ y''(x) f\left (y'(x)\right )+g(y(x)) y'(x)+h(x)=0 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.183944 (sec), leaf count = 0 , could not solve
DSolve[h[x] + g[y[x]]*Derivative[1][y][x] + f[Derivative[1][y][x]]*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 10.899 (sec), leaf count = 0 , result contains DESol or ODESolStruc
\[[]\]
Mathematica raw input
DSolve[h[x] + g[y[x]]*y'[x] + f[y'[x]]*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[h[x] + g[y[x]]*Derivative[1][y][x] + f[Derivative[1][y][x]]*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(f(diff(y(x),x))*diff(diff(y(x),x),x)+g(y(x))*diff(y(x),x)+h(x) = 0, y(x))
Maple raw output
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