\[ a \tan (x) y'(x)+b y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.352534 (sec), leaf count = 129
\[\left \{\left \{y(x)\to c_1 \, _2F_1\left (\frac {1}{4} \left (-a-\sqrt {a^2+4 b}\right ),\frac {1}{4} \left (\sqrt {a^2+4 b}-a\right );\frac {1-a}{2};\cos ^2(x)\right )+i^{a+1} c_2 \cos ^{a+1}(x) \, _2F_1\left (\frac {1}{4} \left (a-\sqrt {a^2+4 b}+2\right ),\frac {1}{4} \left (a+\sqrt {a^2+4 b}+2\right );\frac {a+3}{2};\cos ^2(x)\right )\right \}\right \}\]
✓ Maple : cpu = 0.322 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) = \left ( \cos \left ( x \right ) \right ) ^{{\frac {1}{2}}+{\frac {a}{2}}} \left ( {\it LegendreQ} \left ( {\frac {1}{2}\sqrt {{a}^{2}+4\,b}}-{\frac {1}{2}},{\frac {1}{2}}+{\frac {a}{2}},\sin \left ( x \right ) \right ) {\it \_C2}+{\it LegendreP} \left ( {\frac {1}{2}\sqrt {{a}^{2}+4\,b}}-{\frac {1}{2}},{\frac {1}{2}}+{\frac {a}{2}},\sin \left ( x \right ) \right ) {\it \_C1} \right ) \right \} \]