\[ a y'(x)+b y(x)-f(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.519657 (sec), leaf count = 207
\[\left \{\left \{y(x)\to e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}-a\right )} \int _1^x \frac {f(K[2]) \exp \left (\frac {1}{2} \left (-\sqrt {a^2-4 b}-a\right ) K[2]+a K[2]\right )}{\sqrt {a^2-4 b}} \, dK[2]+e^{\frac {1}{2} x \left (-\sqrt {a^2-4 b}-a\right )} \int _1^x -\frac {f(K[1]) e^{\frac {1}{2} \left (\sqrt {a^2-4 b}-a\right ) K[1]+a K[1]}}{\sqrt {a^2-4 b}} \, dK[1]+c_1 e^{\frac {1}{2} x \left (-\sqrt {a^2-4 b}-a\right )}+c_2 e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}-a\right )}\right \}\right \}\] ✓ Maple : cpu = 0.294 (sec), leaf count = 124
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x}{2} \left ( a-\sqrt {{a}^{2}-4\,b} \right ) }}}{\it \_C2}+{{\rm e}^{-{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}{\it \_C1}+{1 \left ( \int \!f \left ( x \right ) {{\rm e}^{-{\frac {x}{2} \left ( -a+\sqrt {{a}^{2}-4\,b} \right ) }}}\,{\rm d}x{{\rm e}^{x\sqrt {{a}^{2}-4\,b}}}-\int \!f \left ( x \right ) {{\rm e}^{{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}\,{\rm d}x \right ) {{\rm e}^{-{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}{\frac {1}{\sqrt {{a}^{2}-4\,b}}}} \right \} \]