\[ a \tan (x) y'(x)+b y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.254935 (sec), leaf count = 143
\[\left \{\left \{y(x)\to i^{a+1} c_2 \cos ^{a+1}(x) \, _2F_1\left (\frac {a}{4}-\frac {1}{4} \sqrt {a^2+4 b}+\frac {1}{2},\frac {a}{4}+\frac {1}{4} \sqrt {a^2+4 b}+\frac {1}{2};\frac {a}{2}+\frac {3}{2};\cos ^2(x)\right )+c_1 \, _2F_1\left (-\frac {a}{4}-\frac {1}{4} \sqrt {a^2+4 b},\frac {1}{4} \sqrt {a^2+4 b}-\frac {a}{4};\frac {1}{2}-\frac {a}{2};\cos ^2(x)\right )\right \}\right \}\] ✓ Maple : cpu = 0.68 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) = \left ( \cos \left ( x \right ) \right ) ^{{\frac {1}{2}}+{\frac {a}{2}}} \left ( {\it LegendreP} \left ( {\frac {1}{2}\sqrt {{a}^{2}+4\,b}}-{\frac {1}{2}},{\frac {1}{2}}+{\frac {a}{2}},\sin \left ( x \right ) \right ) {\it \_C1}+{\it LegendreQ} \left ( {\frac {1}{2}\sqrt {{a}^{2}+4\,b}}-{\frac {1}{2}},{\frac {1}{2}}+{\frac {a}{2}},\sin \left ( x \right ) \right ) {\it \_C2} \right ) \right \} \]