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Chapter 7: Q13E (page 404)

Find the Laplace transform off(t)=鈭�0t(t鈭�v)e3vdv

Short Answer

Expert verified

Laplace transformation of鈭�0tevsin(t鈭�v)dv is 1s2(s鈭�3).

Step by step solution

01

Assuming g(t) and h(t).

Let

g(t)=th(t)=e3t

02

Getting the values of G(s) and H(s).

Now,

G(s)=L{g(t)}(s)=1s2

H(s)=L{h(t)}(s)=1s鈭�3

03

Step 3: Now, On applying the Convolution Theorem

We get,

L{f(t)}(s)=L{鈭�0t(t鈭�v)e3vdv}(s)=L{鈭�0tg(t鈭�v)h(v)dv}

L{f(t)}(s)=L{g(t)鈭�h(t)}(s)=G(s)鈰�H(s)=1s2(s鈭�3)

Therefore,

L{f(t)}(s)=1s2(s鈭�3)

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Most popular questions from this chapter

In Problems 25 - 32, solve the given initial value problem using the method of Laplace transforms.

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