 Solution

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

For a function for which the integral converges, the Laplace transform is

\overset{ˉ}{f} (p) = \int_{0}^{\infty} e^{- pt} f (t) d t .

For a continuous function of exponential order this exists in a sufficiently far right half-plane. For the first input,

\overline{1} (p) = \frac{1}{p} (Re p > 0) .

This follows by evaluating the exponential antiderivative and using its decay at infinity.

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