\[ a y'(x)+b y(x)+y''(x)+\tan (x)=0 \] ✓ Mathematica : cpu = 0.559657 (sec), leaf count = 502
\[\left \{\left \{y(x)\to \frac {e^{-\frac {1}{2} x \left (\sqrt {a^2-4 b}+a\right )} \left ((2 a-i (b-4)) \left (2 i b \sqrt {a^2-4 b} \left (c_2 e^{x \sqrt {a^2-4 b}}+c_1\right )+\left (\sqrt {a^2-4 b}+a\right ) e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}+a\right )} \, _2F_1\left (1,\frac {1}{4} i \left (\sqrt {a^2-4 b}-a\right );\frac {1}{4} i \left (\sqrt {a^2-4 b}-a\right )+1;-e^{2 i x}\right )+\left (\sqrt {a^2-4 b}-a\right ) e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}+a\right )} \, _2F_1\left (1,-\frac {1}{4} i \left (a+\sqrt {a^2-4 b}\right );\frac {1}{4} \left (-i a-i \sqrt {a^2-4 b}+4\right );-e^{2 i x}\right )\right )+b \left (i \sqrt {a^2-4 b}-i a+4\right ) e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}+a+4 i\right )} \, _2F_1\left (1,-\frac {i a}{4}-\frac {1}{4} i \sqrt {a^2-4 b}+1;-\frac {i a}{4}-\frac {1}{4} i \sqrt {a^2-4 b}+2;-e^{2 i x}\right )+i b \left (\sqrt {a^2-4 b}+a+4 i\right ) e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}+a+4 i\right )} \, _2F_1\left (1,-\frac {i a}{4}+\frac {1}{4} i \sqrt {a^2-4 b}+1;-\frac {i a}{4}+\frac {1}{4} i \sqrt {a^2-4 b}+2;-e^{2 i x}\right )\right )}{2 b \sqrt {a^2-4 b} (2 i a+b-4)}\right \}\right \}\]
✓ Maple : cpu = 0.296 (sec), leaf count = 125
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x}{2} \left ( a-\sqrt {{a}^{2}-4\,b} \right ) }}}{\it \_C2}+{{\rm e}^{-{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}{\it \_C1}-{1 \left ( \int \!\tan \left ( x \right ) {{\rm e}^{-{\frac {x}{2} \left ( -a+\sqrt {{a}^{2}-4\,b} \right ) }}}\,{\rm d}x{{\rm e}^{x\sqrt {{a}^{2}-4\,b}}}-\int \!\tan \left ( x \right ) {{\rm e}^{{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}\,{\rm d}x \right ) {{\rm e}^{-{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}{\frac {1}{\sqrt {{a}^{2}-4\,b}}}} \right \} \]