\[ y(x) \left (a+\frac {f'(x)}{2}+\frac {f(x)^2}{4}\right )+f(x) y'(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0704051 (sec), leaf count = 73
\[\left \{\left \{y(x)\to c_1 \exp \left (-\frac {1}{2} \int _1^x f(K[1]) \, dK[1]-\sqrt {-a} x\right )+\frac {c_2 e^{\sqrt {-a} x-\frac {1}{2} \int _1^x f(K[1]) \, dK[1]}}{2 \sqrt {-a}}\right \}\right \}\]
✓ Maple : cpu = 0.03 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {\int \!f \left ( x \right ) \,{\rm d}x}{2}}}}\sinh \left ( \sqrt {-a}x \right ) +{\it \_C2}\,{{\rm e}^{-{\frac {\int \!f \left ( x \right ) \,{\rm d}x}{2}}}}\cosh \left ( \sqrt {-a}x \right ) \right \} \]