- #1
moo5003
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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
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 }