\[ 4 y''(x)+4 \tan (x) y'(x)+y(x) \left (-5 \tan ^2(x)-2\right )=0 \] ✓ Mathematica : cpu = 0.0680934 (sec), leaf count = 180
DSolve[(-2 - 5*Tan[x]^2)*y[x] + 4*Tan[x]*Derivative[1][y][x] + 4*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {3 (-1)^{5/8} c_2 \left (4 \sqrt [4]{-1} 2^{3/4} \sinh ^{-1}\left (\frac {1}{2} \sqrt [4]{-\frac {1}{2}} \sqrt [4]{-8 \cos ^2(2 x)-16 \cos (2 x)-8}\right )-i \sqrt [4]{-8 \cos ^2(2 x)-16 \cos (2 x)-8} \sqrt {8+i \sqrt {2} \sqrt {-8 \cos ^2(2 x)-16 \cos (2 x)-8}}\right )}{8 \sqrt [8]{2} \sqrt [8]{-8 \cos ^2(2 x)-16 \cos (2 x)-8}}-\frac {(-1)^{7/8} 2^{5/8} c_1}{\sqrt [8]{-8 \cos ^2(2 x)-16 \cos (2 x)-8}}\right \}\right \}\] ✓ Maple : cpu = 0.131 (sec), leaf count = 31
dsolve(4*diff(diff(y(x),x),x)+4*diff(y(x),x)*tan(x)-(5*tan(x)^2+2)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {i \sin \left (x \right ) \cos \left (x \right ) c_{2}-\ln \left (i \cos \left (x \right )+\sin \left (x \right )\right ) c_{2}+c_{1}}{\sqrt {\cos \left (x \right )}}\]