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