4.2.11 \(y'(x)=a y(x)+b y(x)^2+f(x)\)

ODE
\[ y'(x)=a y(x)+b y(x)^2+f(x) \] ODE Classification

[_Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 9.75091 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] == f[x] + a*y[x] + b*y[x]^2, y[x], x]

Maple
cpu = 0.397 (sec), leaf count = 0 , could not solve

dsolve(diff(y(x),x) = f(x)+a*y(x)+b*y(x)^2, y(x),'implicit')

Mathematica raw input

DSolve[y'[x] == f[x] + a*y[x] + b*y[x]^2,y[x],x]

Mathematica raw output

DSolve[Derivative[1][y][x] == f[x] + a*y[x] + b*y[x]^2, y[x], x]

Maple raw input

dsolve(diff(y(x),x) = f(x)+a*y(x)+b*y(x)^2, y(x),'implicit')

Maple raw output

dsolve(diff(y(x),x) = f(x)+a*y(x)+b*y(x)^2, y(x),'implicit')