Let f(x) be a positive function such that the area bounded by y=f(x), y=0 from x=0 to x=a>0 is e^-a+4 a^2+a-1. Then the differential equation, whose…

Let $\displaystyle f(x)$ be a positive function such that the area bounded by $\displaystyle y=f(x), y=0$ from $\displaystyle x=0$ to $\displaystyle x=a>0$ is $\displaystyle e^{-a}+4 a^2+a-1$. Then the differential equation, whose general solution is $\displaystyle y=c_1 f(x)+c_2$, where $\displaystyle c_1$ and $\displaystyle c_2$ are arbitrary constants, is