4.5.15 $x{y}^{\prime }(x)=(y(x{)}^2+1)(x^2+{\tan }^{-1}(y(x)))$

ODE
$$x{y}^{\prime }(x)=(y(x{)}^2+1)(x^2+{\tan }^{-1}(y(x)))$$ ODE Classification

[`y=_G(x,y')`]

Book solution method
Change of Variable, new dependent variable

Mathematica ✓
cpu = 0.0399848 (sec), leaf count = 14

$$\left\{\{y(x)\to \tan \left(x(2c_1+x)\right)\}\right\}$$

Maple ✓
cpu = 0.112 (sec), leaf count = 17

$$\{\frac{\arctan \left(y\left(x\right)\right)}{x}-x-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[x*y'[x] == (x^2 + ArcTan[y[x]])*(1 + y[x]^2),y[x],x]

Mathematica raw output

{{y[x] -> Tan[x*(x + 2*C[1])]}}

Maple raw input

dsolve(x*diff(y(x),x) = (1+y(x)^2)*(x^2+arctan(y(x))), y(x),'implicit')

Maple raw output

1/x*arctan(y(x))-x-_C1 = 0