\[ y(x) \left (a+\frac {f'(x)}{2}+\frac {f(x)^2}{4}\right )+f(x) y'(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0359333 (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 = 0.075 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {\int \!f \left ( x \right ) \,{\rm d}x}{2}}}} \left ( \sinh \left ( \sqrt {-a}x \right ) {\it \_C1}+\cosh \left ( \sqrt {-a}x \right ) {\it \_C2} \right ) \right \} \]