\[ a y'(x)+b y(x)-f(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.527777 (sec), leaf count = 150
\[\left \{\left \{y(x)\to e^{-\frac {1}{2} x \left (\sqrt {a^2-4 b}+a\right )} \left (\int _1^x -\frac {f(K[1]) e^{\frac {1}{2} \left (\sqrt {a^2-4 b}+a\right ) K[1]}}{\sqrt {a^2-4 b}} \, dK[1]+e^{x \sqrt {a^2-4 b}} \int _1^x \frac {f(K[2]) e^{\frac {1}{2} \left (a-\sqrt {a^2-4 b}\right ) K[2]}}{\sqrt {a^2-4 b}} \, dK[2]+c_2 e^{x \sqrt {a^2-4 b}}+c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.357 (sec), leaf count = 124
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x}{2} \left ( a-\sqrt {{a}^{2}-4\,b} \right ) }}}{\it \_C2}+{{\rm e}^{-{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}{\it \_C1}+{1 \left ( \int \!f \left ( x \right ) {{\rm e}^{-{\frac {x}{2} \left ( -a+\sqrt {{a}^{2}-4\,b} \right ) }}}\,{\rm d}x{{\rm e}^{x\sqrt {{a}^{2}-4\,b}}}-\int \!f \left ( x \right ) {{\rm e}^{{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}\,{\rm d}x \right ) {{\rm e}^{-{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}{\frac {1}{\sqrt {{a}^{2}-4\,b}}}} \right \} \]