How to solve this initial value problem? Or is it really an initial value probem?

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I have peculiar kind of initial value problem, and I don't know how to proceed. The problem is as follow: $$\frac{dw(\epsilon,t)}{d\epsilon}\bigg|_{\epsilon=0}=f(t).$$ Here $w(\epsilon, t)$ is function of both $\epsilon$ and $t$. Please suggest if there is any way to solve above initial problem.