4.37.5 \(y'(x) f(x,y(x))+g(x,y(x))+y''(x)=0\)

ODE
\[ y'(x) f(x,y(x))+g(x,y(x))+y''(x)=0 \] ODE Classification

[NONE]

Book solution method
TO DO

Mathematica
cpu = 0.584661 (sec), leaf count = 0 , could not solve

DSolve[g[x, y[x]] + f[x, y[x]]*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]

Maple
cpu = 0.004 (sec), leaf count = 0 , could not solve

dsolve(diff(diff(y(x),x),x)+f(x,y(x))*diff(y(x),x)+g(x,y(x)) = 0, y(x),'implicit')

Mathematica raw input

DSolve[g[x, y[x]] + f[x, y[x]]*y'[x] + y''[x] == 0,y[x],x]

Mathematica raw output

DSolve[g[x, y[x]] + f[x, y[x]]*Derivative[1][y][x] + Derivative[2][y][x] == 0, y
[x], x]

Maple raw input

dsolve(diff(diff(y(x),x),x)+f(x,y(x))*diff(y(x),x)+g(x,y(x)) = 0, y(x),'implicit')

Maple raw output

dsolve(diff(diff(y(x),x),x)+f(x,y(x))*diff(y(x),x)+g(x,y(x)) = 0, y(x),'implicit
')