\[ y''(x)=\left (3 \sin ^2(x)+1\right ) \csc (x) \sec (x) y'(x)+y(x) \tan ^2(x) \] ✓ Mathematica : cpu = 0.237698 (sec), leaf count = 42
DSolve[Derivative[2][y][x] == Tan[x]^2*y[x] + Csc[x]*Sec[x]*(1 + 3*Sin[x]^2)*Derivative[1][y][x],y[x],x]
\[\left \{\left \{y(x)\to c_2 \cos ^{\frac {1}{2} \left (\sqrt {13}-3\right )}(x)+c_1 \cos ^{\frac {1}{2} \left (-3-\sqrt {13}\right )}(x)\right \}\right \}\] ✓ Maple : cpu = 0.167 (sec), leaf count = 29
dsolve(diff(diff(y(x),x),x) = (3*sin(x)^2+1)/cos(x)/sin(x)*diff(y(x),x)+sin(x)^2/cos(x)^2*y(x),y(x))
\[y \left (x \right ) = c_{1} \left (\cos ^{-\frac {3}{2}+\frac {\sqrt {13}}{2}}\left (x \right )\right )+c_{2} \left (\cos ^{-\frac {3}{2}-\frac {\sqrt {13}}{2}}\left (x \right )\right )\]