2.1422   ODE No. 1422

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

✓ Mathematica : cpu = 0.103934 (sec), leaf count = 64

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

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

✓ Maple : cpu = 0.325 (sec), leaf count = 50

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

\[y \left (x \right ) = \frac {i \sin \left (2 x \right ) \ln \left (\cos \left (2 x \right )+i \sin \left (2 x \right )\right ) c_{2} +\left (\cos \left (2 x \right )-1\right ) \left (c_{1} \cot \left (x \right )-2 c_{2} \right )}{\cos \left (2 x \right )-1}\]