Suppose $f(i,t): R^+\times R^+ \rightarrow R^+$, $f(0, t)=1$ and $h(i)$ is a given function like $h(i)=(1+i)^{-2}$
How would I find $f$ satisfying the following differential equation?
$$\int \mathrm{d}i\ \frac{d}{dt} f(i, t) h(i) = -2\int \mathrm{d} i\ h(i)^2 f(i, t) + \int \mathrm{d} i\ h(i) f(i, t)$$