2.1417   ODE No. 1417

\[ y''(x)=-\csc (x) y'(x) \left (\sin ^2(x)-\cos (x)\right )-y(x) \sin ^2(x) \] Mathematica : cpu = 0.0955429 (sec), leaf count = 52

DSolve[Derivative[2][y][x] == -(Sin[x]^2*y[x]) - Csc[x]*(-Cos[x] + Sin[x]^2)*Derivative[1][y][x],y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{\frac {\cos (x)}{2}} \cos \left (\frac {1}{2} \sqrt {3} \cos (x)\right )+c_2 e^{\frac {\cos (x)}{2}} \sin \left (\frac {1}{2} \sqrt {3} \cos (x)\right )\right \}\right \}\] Maple : cpu = 0.165 (sec), leaf count = 31

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

\[y \left (x \right ) = {\mathrm e}^{\frac {\cos \left (x \right )}{2}} \left (\sin \left (\frac {\sqrt {3}\, \cos \left (x \right )}{2}\right ) c_{1}+\cos \left (\frac {\sqrt {3}\, \cos \left (x \right )}{2}\right ) c_{2}\right )\]