\[ y(x) \left (a+\frac {f'(x)}{2}+\frac {f(x)^2}{4}\right )+f(x) y'(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0688608 (sec), leaf count = 74
\[\left \{\left \{y(x)\to c_1 e^{-\frac {1}{2} \int _1^x f(K[1]) \, dK[1]-i \sqrt {a} x}-\frac {i c_2 e^{-\frac {1}{2} \int _1^x f(K[1]) \, dK[1]+i \sqrt {a} x}}{2 \sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.059 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {\int \!f \left ( x \right ) \,{\rm d}x}{2}}}} \left ( \sinh \left ( \sqrt {-a}x \right ) {\it \_C1}+\cosh \left ( \sqrt {-a}x \right ) {\it \_C2} \right ) \right \} \]