\[ y(x) (a+x \cot (x))+x^2 y''(x)+\left (2 x^2 \cot (x)+x\right ) y'(x)=0 \] ✓ Mathematica : cpu = 0.0819408 (sec), leaf count = 38
DSolve[(a + x*Cot[x])*y[x] + (x + 2*x^2*Cot[x])*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \csc (x) \operatorname {BesselJ}\left (i \sqrt {a},x\right )+c_2 \csc (x) \operatorname {BesselY}\left (i \sqrt {a},x\right )\right \}\right \}\] ✓ Maple : cpu = 0.058 (sec), leaf count = 28
dsolve(x^2*diff(diff(y(x),x),x)+(2*x^2*cot(x)+x)*diff(y(x),x)+(x*cot(x)+a)*y(x)=0,y(x))
\[y \left (x \right ) = \csc \left (x \right ) \left (\operatorname {BesselY}\left (i \sqrt {a}, x\right ) c_{2}+\operatorname {BesselJ}\left (i \sqrt {a}, x\right ) c_{1}\right )\]