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

Jakobe Norton
2022-04-15
Answered

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

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stecchiniror7

Answered 2022-04-16
Author has **14** answers

We have:

$\mathcal{L}\left(t\right)=\frac{1}{{s}^{2}}$

Thus, we have:

$\mathcal{L}\left(10t{e}^{-5t}\right)=10F(s+5)=\frac{10}{{(s+5)}^{2}}$

Note: we made use of the Shifting Theorem, which was mentioned to you in another post.

Thus, we have:

Note: we made use of the Shifting Theorem, which was mentioned to you in another post.

granfury90210birm

Answered 2022-04-17
Author has **10** answers

HINT:

Use

$L\left\{{e}^{at}f\left(t\right)\right\}=F(s-a)\text{}\text{if}\text{}L\left\{f\left(t\right)\right\}=F\left(s\right)$

and

$L\left({t}^{n}\right)=\frac{\mathrm{\Gamma}(n+1)}{{s}^{n+1}}$

and

$\mathrm{\Gamma}(n+1)=n!$ if n is non-negative integer

Use

and

and

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Exact Differential Equations

Instructions:

Solve the Exact Differential Equations of GIven Problem #2 only, ignore the other given problem.

Note:

Please answer all of the problems in the attached photo. I will rate you with “like/upvote” after; if you answer all of the problems. If not, I will rate you “unlike/downvote.” Kindly show the complete step-by-step solution.

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Exact Differential Equations

Instructions:

Solve the Exact Differential Equations of GIven Problem #2 only, ignore the other given problem.

Note:

Please answer all of the problems in the attached photo. I will rate you with “like/upvote” after; if you answer all of the problems. If not, I will rate you “unlike/downvote.” Kindly show the complete step-by-step solution.

1.

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