4.2.47 \(y'(x)=f(x)+g(x) y(x)+h(x) y(x)^n\)

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

[_Chini]

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 3.99729 (sec), leaf count = 0 , could not solve

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

Maple
cpu = 0.36 (sec), leaf count = 0 , could not solve

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

Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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