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 = 8.1222 (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 = 0.292 (sec), leaf count = 0 , could not solve
dsolve(y(x)*diff(y(x),x)+f(x) = g(x)*y(x), y(x))
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))
Maple raw output
dsolve(y(x)*diff(y(x),x)+f(x) = g(x)*y(x), y(x))