ODE
\[ y'(x)=a y(x)^2+f(x)+g(x) y(x) \] ODE Classification
[_Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✗
cpu = 20.8632 (sec), leaf count = 0 , could not solve
DSolve[Derivative[1][y][x] == f[x] + g[x]*y[x] + a*y[x]^2, y[x], x]
Maple ✗
cpu = 0.213 (sec), leaf count = 0 , could not solve
dsolve(diff(y(x),x) = f(x)+g(x)*y(x)+a*y(x)^2, y(x),'implicit')
Mathematica raw input
DSolve[y'[x] == f[x] + g[x]*y[x] + a*y[x]^2,y[x],x]
Mathematica raw output
DSolve[Derivative[1][y][x] == f[x] + g[x]*y[x] + a*y[x]^2, y[x], x]
Maple raw input
dsolve(diff(y(x),x) = f(x)+g(x)*y(x)+a*y(x)^2, y(x),'implicit')
Maple raw output
dsolve(diff(y(x),x) = f(x)+g(x)*y(x)+a*y(x)^2, y(x),'implicit')