\[ y(x) \left (a+\frac {f'(x)}{2}+\frac {f(x)^2}{4}\right )+f(x) y'(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0304972 (sec), leaf count = 76
DSolve[y[x]*(a + f[x]^2/4 + Derivative[1][f][x]/2) + f[x]*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \exp \left (-\frac {1}{2} \int _1^xf(K[1])dK[1]-i \sqrt {a} x\right )-\frac {i c_2 \exp \left (-\frac {1}{2} \int _1^xf(K[1])dK[1]+i \sqrt {a} x\right )}{2 \sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.035 (sec), leaf count = 33
dsolve(diff(diff(y(x),x),x)+f(x)*diff(y(x),x)+(1/4*f(x)^2+1/2*diff(f(x),x)+a)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {\left (\int f \left (x \right )d x \right )}{2}} \left (\sinh \left (\sqrt {-a}\, x \right ) c_{1}+\cosh \left (\sqrt {-a}\, x \right ) c_{2}\right )\]