2.1429   ODE No. 1429

\[ y''(x)=y(x) \csc ^2(x)-\cot (x) y'(x) \]

✓ Mathematica : cpu = 0.0330725 (sec), leaf count = 41

DSolve[Derivative[2][y][x] == Csc[x]^2*y[x] - Cot[x]*Derivative[1][y][x],y[x],x]
 

\[\left \{\left \{y(x)\to \frac {c_1}{\sqrt {1-\cos ^2(x)}}-\frac {i c_2 \cos (x)}{\sqrt {1-\cos ^2(x)}}\right \}\right \}\]

✓ Maple : cpu = 0.042 (sec), leaf count = 21

dsolve(diff(diff(y(x),x),x) = -1/sin(x)*cos(x)*diff(y(x),x)+1/sin(x)^2*y(x),y(x))
 

\[y \left (x \right ) = c_{1} \left (\csc \left (x \right )+\cot \left (x \right )\right )+\frac {c_{2}}{\csc \left (x \right )+\cot \left (x \right )}\]