4.7.6 \(\left (x^2+1\right ) y'(x)=x^2-y(x) \cot ^{-1}(x)+1\)

ODE
\[ \left (x^2+1\right ) y'(x)=x^2-y(x) \cot ^{-1}(x)+1 \] 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

\[ \left \{ y \relax (x ) = \left (\int \!{{\rm e}^{-{\frac { \left (\pi -2\,\arctan \relax (x ) \right ) ^{2}}{8}}}}\,{\rm d}x+{\it \_C1} \right ) {{\rm e}^{{\frac { \left ({\rm arccot} \relax (x) \right ) ^{2}}{2}}}} \right \} \] 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)