2.1008   ODE No. 1008

\[ a^2 y(x)-\cot (a x)+y''(x)=0 \]

✓ Mathematica : cpu = 0.0427087 (sec), leaf count = 48

DSolve[-Cot[a*x] + a^2*y[x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {\sin (a x) \left (\log \left (\cos \left (\frac {a x}{2}\right )\right )-\log \left (\sin \left (\frac {a x}{2}\right )\right )\right )}{a^2}+c_1 \cos (a x)+c_2 \sin (a x)\right \}\right \}\]

✓ Maple : cpu = 0.185 (sec), leaf count = 37

dsolve(diff(diff(y(x),x),x)+a^2*y(x)-cot(a*x)=0,y(x))
 

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