Find the Laplace transform of \(\displaystyle{f{{\left({t}\right)}}}={10}{t}{e}^{{-{5}{t}}}\)

Jakobe Norton

Jakobe Norton

Answered question

2022-04-15

Find the Laplace transform of f(t)=10te5t

Answer & Explanation

stecchiniror7

stecchiniror7

Beginner2022-04-16Added 14 answers

We have:
L(t)=1s2
Thus, we have:
L(10te5t)=10F(s+5)=10(s+5)2
Note: we made use of the Shifting Theorem, which was mentioned to you in another post.
granfury90210birm

granfury90210birm

Beginner2022-04-17Added 10 answers

HINT:
Use
L{eatf(t)}=F(sa)  if  L{f(t)}=F(s)
and
L(tn)=Γ(n+1)sn+1
and
Γ(n+1)=n! if n is non-negative integer

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