\[ a y'(x)+b y(x)-f(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0847113 (sec), leaf count = 209
DSolve[-f[x] + b*y[x] + a*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to e^{\frac {1}{2} x \left (-\sqrt {a^2-4 b}-a\right )} \int _1^x-\frac {e^{a K[1]+\frac {1}{2} \left (\sqrt {a^2-4 b}-a\right ) K[1]} f(K[1])}{\sqrt {a^2-4 b}}dK[1]+e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}-a\right )} \int _1^x\frac {e^{a K[2]+\frac {1}{2} \left (-a-\sqrt {a^2-4 b}\right ) K[2]} f(K[2])}{\sqrt {a^2-4 b}}dK[2]+c_1 e^{\frac {1}{2} x \left (-\sqrt {a^2-4 b}-a\right )}+c_2 e^{\frac {1}{2} x \left (\sqrt {a^2-4 b}-a\right )}\right \}\right \}\] ✓ Maple : cpu = 0.108 (sec), leaf count = 134
dsolve(diff(diff(y(x),x),x)+a*diff(y(x),x)+b*y(x)-f(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {\left (a -\sqrt {a^{2}-4 b}\right ) x}{2}} c_{2}+{\mathrm e}^{-\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}} c_{1}+\frac {{\mathrm e}^{-a x} \left (\left (\int f \left (x \right ) {\mathrm e}^{-\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}}d x \right ) {\mathrm e}^{\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}}-\left (\int f \left (x \right ) {\mathrm e}^{\frac {\left (a +\sqrt {a^{2}-4 b}\right ) x}{2}}d x \right ) {\mathrm e}^{-\frac {\left (-a +\sqrt {a^{2}-4 b}\right ) x}{2}}\right )}{\sqrt {a^{2}-4 b}}\]