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Exercise 18

Avg difficulty 2.5

Let ff be a function whose Laplace transform L(f)(s)=F(s){\mathcal L}(f)(s)= F(s) exists for s>as \gt a. Prove that L(ectf(t))(s)=F(s−c){\mathcal L}(e^{ct} f(t))(s)= F(s - c) for s>a+cs \gt a + c.

Judson, The ODE Project, §6.1 The Laplace Transform, Exercise 18

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Adapted from The ODE Project © 2019–2025 Thomas W. Judson. Licensed under CC BY 4.0. Source: The ODE Project. Imported at revision 7935458.