2.1024   ODE No. 1024

\[ y''(x)+y(x) \left (-2 \tan ^2(x)-1\right )=0 \]

✓ Mathematica : cpu = 0.166874 (sec), leaf count = 52

DSolve[(-1 - 2*Tan[x]^2)*y[x] + Derivative[2][y][x] == 0,y[x],x]
 

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

✓ Maple : cpu = 0.24 (sec), leaf count = 28

dsolve(diff(diff(y(x),x),x)-(1+2*tan(x)^2)*y(x)=0,y(x))
 

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