\[ y''(x)=y(x) \csc ^2(x)-\cot (x) y'(x) \] ✓ Mathematica : cpu = 0.0387498 (sec), leaf count = 51
DSolve[Derivative[2][y][x] == Csc[x]^2*y[x] - Cot[x]*Derivative[1][y][x],y[x],x]
\[\left \{\left \{y(x)\to c_1 \cosh \left (\log \left (\cos \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )\right )\right )-i c_2 \sinh \left (\log \left (\cos \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.04 (sec), leaf count = 25
dsolve(diff(diff(y(x),x),x) = -1/sin(x)*cos(x)*diff(y(x),x)+1/sin(x)^2*y(x),y(x))
\[y \left (x \right ) = \frac {\sin \left (x \right ) c_{1}}{\cos \left (x \right )-1}+\frac {\left (\cos \left (x \right )-1\right ) c_{2}}{\sin \left (x \right )}\]