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**1. Homework Statement**

U is a function of x and t

d/dt(U) = d/dx(U) + V(x,t)U

U(x,0) = f(x)

Suppose:

U(x,t) = e^(Integral from 0 to 1 [V(x+s,t-s)]ds) * f(x+t)

Show directly (no change of variables) that this solves the above PDE

Show using change of variables that this solves the above PDE letting

Alpha = x+t

Gamma = x-t

**3. The Attempt at a Solution**

My main question is how to evlauate d/dt { Integral from 0 to 1 [V(x+s,t-s)]ds }