4.7.6 $(x^2+1)y^{\prime }(x)=x^2-y(x){\cot }^{-1}(x)+1$

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

[_linear]

Book solution method
Linear ODE

Mathematica ✗
cpu = 599.991 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.33 (sec), leaf count = 27

$$\{y\left(x\right)=(\int {\mathrm{e}}^{-\frac{{(\pi -2\arctan \left(x\right))}^2}{8}}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1}){\mathrm{e}}^{\frac{{\left(\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{c}\mathrm{o}\mathrm{t}\left(x\right)\right)}^2}{2}}\}$$ Mathematica raw input

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

y(x) = (Int(exp(-1/8*(Pi-2*arctan(x))^2),x)+_C1)*exp(1/2*arccot(x)^2)