\[ a y'(x)+b y(x)-f(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.130587 (sec), leaf count = 209
\[\left \{\left \{y(x)\to e^{\frac {1}{2} x \left (-\sqrt {a^2-4 b}-a\right )} \int _1^x-\frac {e^{a K[1]+\frac {1}{2} \left (\sqrt {a^2-4 b}-a\right ) K[1]} f(K[1])}{\sqrt {a^2-4 b}}dK[1]+e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}-a\right )} \int _1^x\frac {e^{a K[2]+\frac {1}{2} \left (-a-\sqrt {a^2-4 b}\right ) K[2]} f(K[2])}{\sqrt {a^2-4 b}}dK[2]+c_1 e^{\frac {1}{2} x \left (-\sqrt {a^2-4 b}-a\right )}+c_2 e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}-a\right )}\right \}\right \}\] ✓ Maple : cpu = 0.214 (sec), leaf count = 124
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x}{2} \left ( a-\sqrt {{a}^{2}-4\,b} \right ) }}}{\it \_C2}+{{\rm e}^{-{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}{\it \_C1}+{ \left ( \int \!f \left ( x \right ) {{\rm e}^{-{\frac {x}{2} \left ( -a+\sqrt {{a}^{2}-4\,b} \right ) }}}\,{\rm d}x{{\rm e}^{x\sqrt {{a}^{2}-4\,b}}}-\int \!f \left ( x \right ) {{\rm e}^{{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}\,{\rm d}x \right ) {{\rm e}^{-{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}}{\frac {1}{\sqrt {{a}^{2}-4\,b}}}} \right \} \]