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http://users.on.net/~rohanlal/laplacetrans5.jpg [Broken]

In the third line, what is S+4 the laplace transform of?

In the third line, what is S+4 the laplace transform of?

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- Thread starter Ry122
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In the third line, what is S+4 the laplace transform of?

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In the third line, what is S+4 the laplace transform of?

It doesn't matter. Just isolate Y(s) by dividing both sides by (s+4). Then use partial fractions to compute the inverse Laplace Transform of the RHS.

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As Gabbagabbahey said, you need to divide both sides by s+ 4 to get

[tex]Y(s)= \frac{17}{(s^2+1)(s+4)}+ \frac{1}{s+4}[/tex]

Partial fractions will give something of the form

[tex]Y(s)= \frac{As}{s^2+1}+ \frac{B}{s^2+1}+ \frac{C}{s+4}[/tex]

and then you can look up the inverse transform of each of those.

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so is the laplace transform of 4y = 1/s+4? then how does it end up being a factor of y(s)?

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so is the laplace transform of 4y = 1/s+4? then how does it end up being a factor of y(s)?

I'm not exactly sure what you are trying to ask here. If you are asking whether [itex]4Y(s)=\frac{1}{s+4}[/itex], then the answer is no.

You have correctly gotten to this point:

[tex](s+4)Y(s)=\frac{17}{s^2+1}+1[/tex]

However, for this to be useful you need to divide both sides of the equation by [itex]s+4[/itex] in order to isolate [itex]Y(s)[/itex]. The reason why simply taking the inverse Laplace transform of both sides in the current form is useless is because [itex]\mathcal{L}^{-1}[(s+4)Y(s)]\neq(\mathcal{L}^{-1}[(s+4)])\cdot(\mathcal{L}^{-1}[Y(s)])[/itex]

But if you divide by [itex]s+4[/itex] first, you get

[tex]Y(s)=\frac{17}{(s^2+1)(s+4)}+\frac{1}{s+4} \implies y(t)=\mathcal{L}^{-1}[Y(s)]=\mathcal{L}^{-1}[\frac{17}{(s^2+1)(s+4)}+\frac{1}{s+4}][/tex]

which allows you to find [itex]y(t)[/itex].

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[tex]

(s+4)Y(s)=\frac{17}{s^2+1}+1

[/tex]

someone else did. i want to know how they got there.

im unsure as to how they got y(s)[s+4]

i also don't know what the laplace transform of 4y is.

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The working i attached wasn't carried out by me. I haven't gotten as far as

[tex]

(s+4)Y(s)=\frac{17}{s^2+1}+1

[/tex]

someone else did. i want to know how they got there.

im unsure as to how they got y(s)[s+4]

i also don't know what the laplace transform of 4y is.

Oh! Now I see what you were asking.

The workings in your attached image should be fairly clear: [itex]\mathcal{L}[4y(t)]=4\mathcal{L}[y(t)]=4Y(s)[/itex] and [itex]\mathcal{L}[y'(t)]=sY(s)-y(0)=sY(s)-1[/itex]. The reasons for this should be in your textbook/notes, and if you are not comfortable with such basic Laplace transforms you need to study your text/notes and perhaps get a tutor.

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