4.9.25 \(f(x)+y(x) y'(x)=g(x) y(x)\)

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

[[_Abel, `2nd type``class A`]]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 9.65825 (sec), leaf count = 0 , could not solve

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

Maple
cpu = 0.24 (sec), leaf count = 0 , could not solve

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

Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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