\[ a \tan (x) y'(x)+b y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.244218 (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 = 0.157 (sec), leaf count = 60
\[y \relax (x ) = \left (\cos ^{\frac {1}{2}+\frac {a}{2}}\relax (x )\right ) \left (\LegendreP \left (\frac {\sqrt {a^{2}+4 b}}{2}-\frac {1}{2}, \frac {1}{2}+\frac {a}{2}, \sin \relax (x )\right ) c_{1}+\LegendreQ \left (\frac {\sqrt {a^{2}+4 b}}{2}-\frac {1}{2}, \frac {1}{2}+\frac {a}{2}, \sin \relax (x )\right ) c_{2}\right )\]