4.1.41 $f(x{)}^2+y^{\prime }(x)=f^{\prime }(x)+y(x{)}^2$

ODE
$$f(x{)}^2+y^{\prime }(x)=f^{\prime }(x)+y(x{)}^2$$ 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

$$\{y\left(x\right)=f\left(x\right)+\frac{{\mathrm{e}}^{\int 2f\left(x\right)\mathrm{d}x}}{\mathit{\_}\mathit{C}\mathit{1}-\int {\mathrm{e}}^{\int 2f\left(x\right)\mathrm{d}x}\mathrm{d}x}\}$$ 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))