\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \tan \left ( x \right ) +by \left ( x \right ) =0} \]
Mathematica: cpu = 0.317540 (sec), leaf count = 143 \[ \left \{\left \{y(x)\to c_1 \, _2F_1\left (-\frac {a}{4}-\frac {1}{4} \sqrt {a^2+4 b},\frac {1}{4} \sqrt {a^2+4 b}-\frac {a}{4};\frac {1}{2}-\frac {a}{2};\cos ^2(x)\right )+i^{a+1} c_2 \cos ^{a+1}(x) \, _2F_1\left (\frac {a}{4}-\frac {1}{4} \sqrt {a^2+4 b}+\frac {1}{2},\frac {a}{4}+\frac {1}{4} \sqrt {a^2+4 b}+\frac {1}{2};\frac {a}{2}+\frac {3}{2};\cos ^2(x)\right )\right \}\right \} \]
Maple: cpu = 0.141 (sec), leaf count = 67 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( \cos \left ( x \right ) \right ) ^{{\frac {1}{2}}+{\frac {a}{2}}}{\it LegendreP} \left ( {\frac {1}{2}\sqrt {{a}^{2}+4\,b}}-{\frac {1}{2}},{\frac {1}{2 }}+{\frac {a}{2}},\sin \left ( x \right ) \right ) +{\it \_C2}\, \left ( \cos \left ( x \right ) \right ) ^{{\frac {1}{2}}+{\frac {a}{2}}}{\it LegendreQ} \left ( {\frac {1}{2}\sqrt {{a}^{2}+4\,b}}-{\frac {1}{2}},{ \frac {1}{2}}+{\frac {a}{2}},\sin \left ( x \right ) \right ) \right \} \]