 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-2-course-of-the-university-of-oxford/2006/differential-equations/9/ii/solution

Re p > 0

, gives

\overline{t} (p) = \int_{0}^{\infty} t e^{- pt} d t = \frac{1}{p} \int_{0}^{\infty} e^{- pt} d t = \frac{1}{p ^{2}} .

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