2.1435   ODE No. 1435

\[ y''(x)=-4 y(x) \sin (3 x) \csc ^3(x) \]

✓ Mathematica : cpu = 0.132559 (sec), leaf count = 70

DSolve[Derivative[2][y][x] == -4*Csc[x]^3*Sin[3*x]*y[x],y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \sqrt [4]{\cos ^2(x)-1} P_{-\frac {1}{2}+4 i}^{\frac {i \sqrt {47}}{2}}(\cos (x))+c_2 \sqrt [4]{\cos ^2(x)-1} Q_{-\frac {1}{2}+4 i}^{\frac {i \sqrt {47}}{2}}(\cos (x))\right \}\right \}\]

✓ Maple : cpu = 0.247 (sec), leaf count = 38

dsolve(diff(diff(y(x),x),x) = -4*sin(3*x)/sin(x)^3*y(x),y(x))
 

\[y \left (x \right ) = \sqrt {\sin \left (x \right )}\, \left (\operatorname {LegendreQ}\left (-\frac {1}{2}+4 i, \frac {i \sqrt {47}}{2}, \cos \left (x \right )\right ) c_{2} +\operatorname {LegendreP}\left (-\frac {1}{2}+4 i, \frac {i \sqrt {47}}{2}, \cos \left (x \right )\right ) c_{1} \right )\]