 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-2-course-of-the-university-of-oxford/2007/9/iii/solution

Integrating the exponential directly gives

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

The inequality is the absolute-convergence domain of this Laplace transform.

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