\[ y(x) (a+x \cot (x))+x^2 y''(x)+\left (2 x^2 \cot (x)+x\right ) y'(x)=0 \] ✓ Mathematica : cpu = 0.107503 (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]
\[\left \{\left \{y(x)\to c_1 \csc (x) J_{i \sqrt {a}}(x)+c_2 \csc (x) Y_{i \sqrt {a}}(x)\right \}\right \}\] ✓ Maple : cpu = 0.044 (sec), leaf count = 30
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))
\[y \left (x \right ) = \frac {c_{2} \BesselY \left (i \sqrt {a}, x\right )+c_{1} \BesselJ \left (i \sqrt {a}, x\right )}{\sin \left (x \right )}\]