Past exam of the algebra, analysis and differential equations II course of the University of Oxford / 2006 / Differential equations / 9 / ii

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- Solution ii

Solution

Integration by parts, whose boundary term vanishes for

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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