 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-2-course-of-the-university-of-oxford/2011/differential-equations/9/ii/solution

Combine the exponentials and integrate:

L [e^{- a t}] (p) = \int_{0}^{\infty} e^{- (p + a) t} d t = \frac{1}{p + a}, Re p > - a .

a > 0

makes this convergence half-plane larger than the one for the constant function.

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