2.1218   ODE No. 1218

\[ y(x) (a+x \cot (x))+x^2 y''(x)+\left (2 x^2 \cot (x)+x\right ) y'(x)=0 \]

✓ Mathematica : cpu = 0.0503573 (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 = 0.083 (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))
 

\[y \left (x \right ) = \csc \left (x \right ) \left (\operatorname {BesselY}\left (i \sqrt {a}, x\right ) c_{2} +\operatorname {BesselJ}\left (i \sqrt {a}, x\right ) c_{1} \right )\]