\[ y(x) \left (a+\frac {f'(x)}{2}+\frac {f(x)^2}{4}\right )+f(x) y'(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0432429 (sec), leaf count = 76
\[\left \{\left \{y(x)\to c_1 \exp \left (-\frac {1}{2} \int _1^xf(K[1])dK[1]-i \sqrt {a} x\right )-\frac {i c_2 \exp \left (-\frac {1}{2} \int _1^xf(K[1])dK[1]+i \sqrt {a} x\right )}{2 \sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.037 (sec), leaf count = 33
\[\left \{y \left (x \right ) = \left (c_{1} \sinh \left (\sqrt {-a}\, x \right )+c_{2} \cosh \left (\sqrt {-a}\, x \right )\right ) {\mathrm e}^{-\frac {\left (\int f \left (x \right )d x \right )}{2}}\right \}\]