4.1.41 \(f(x)^2+y'(x)=f'(x)+y(x)^2\)

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

(ODEtools/info) missing specification of intermediate function

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 13.5635 (sec), leaf count = 0 , could not solve

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

Maple
cpu = 0.635 (sec), leaf count = 30

\[ \left \{ y \relax (x ) =f \relax (x ) +{\frac {{{\rm e}^{\int \!2\,f \relax (x ) \,{\rm d}x}}}{{\it \_C1}-\int \!{{\rm e}^{\int \!2\,f \relax (x ) \,{\rm d}x}}\,{\rm d}x}} \right \} \] Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = f(x)+exp(Int(2*f(x),x))/(_C1-Int(exp(Int(2*f(x),x)),x))