\[ y''(x)+y(x) \left (-2 \tan ^2(x)-1\right )=0 \] ✓ Mathematica : cpu = 0.129848 (sec), leaf count = 84
DSolve[(-1 - 2*Tan[x]^2)*y[x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 \sqrt [4]{1-\cos ^2(x)} \sec (x)}{\sqrt [4]{\cos ^2(x)-1}}-\frac {c_2 \sqrt [4]{1-\cos ^2(x)} \sec (x) \left (\cos (x) \sqrt {1-\cos ^2(x)}-\sin ^{-1}(\cos (x))\right )}{2 \sqrt [4]{\cos ^2(x)-1}}\right \}\right \}\] ✓ Maple : cpu = 0.127 (sec), leaf count = 30
dsolve(diff(diff(y(x),x),x)-(1+2*tan(x)^2)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {i \sin \left (x \right ) \cos \left (x \right ) c_{2}+\ln \left (\cos \left (x \right )+i \sin \left (x \right )\right ) c_{2}+c_{1}}{\cos \left (x \right )}\]