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snow_lady [41]
3 years ago
13

PLEASE HELP ME THIS ANSWER DRIVING ME CRAZY!!!

Mathematics
2 answers:
DaniilM [7]3 years ago
7 0
It’s blurry really blurry yuu needs make it more clear to get to get a answer
shtirl [24]3 years ago
6 0
It’s mad blurry so if you want an answer you have to make it more clear
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Use the laplace transform to solve the given initial-value problem. y' 5y = e4t, y(0) = 2
Basile [38]

The Laplace transform of the given initial-value problem

y' 5y = e^{4t}, y(0) = 2 is  mathematically given as

y(t)=\frac{1}{9} e^{4 t}+\frac{17}{9} e^{-5 t}

<h3>What is the Laplace transform of the given initial-value problem? y' 5y = e4t, y(0) = 2?</h3>

Generally, the equation for the problem is  mathematically given as

&\text { Sol:- } \quad y^{\prime}+s y=e^{4 t}, y(0)=2 \\\\&\text { Taking Laplace transform of (1) } \\\\&\quad L\left[y^{\prime}+5 y\right]=\left[\left[e^{4 t}\right]\right. \\\\&\Rightarrow \quad L\left[y^{\prime}\right]+5 L[y]=\frac{1}{s-4} \\\\&\Rightarrow \quad s y(s)-y(0)+5 y(s)=\frac{1}{s-4} \\\\&\Rightarrow \quad(s+5) y(s)=\frac{1}{s-4}+2 \\\\&\Rightarrow \quad y(s)=\frac{1}{s+5}\left[\frac{1}{s-4}+2\right]=\frac{2 s-7}{(s+5)(s-4)}\end{aligned}

\begin{aligned}&\text { Let } \frac{2 s-7}{(s+5)(s-4)}=\frac{a_{0}}{s-4}+\frac{a_{1}}{s+5} \\&\Rightarrow 2 s-7=a_{0}(s+s)+a_{1}(s-4)\end{aligned}

put $s=-s \Rightarrow a_{1}=\frac{17}{9}$

\begin{aligned}\text { put } s &=4 \Rightarrow a_{0}=\frac{1}{9} \\\Rightarrow \quad y(s) &=\frac{1}{9(s-4)}+\frac{17}{9(s+s)}\end{aligned}

In conclusion, Taking inverse Laplace tranoform

L^{-1}[y(s)]=\frac{1}{9} L^{-1}\left[\frac{1}{s-4}\right]+\frac{17}{9} L^{-1}\left[\frac{1}{s+5}\right]$ \\\\

y(t)=\frac{1}{9} e^{4 t}+\frac{17}{9} e^{-5 t}

Read more about Laplace tranoform

brainly.com/question/14487937

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1 year ago
If you conducted a survey on the distribution of M &amp; M colors in 20 packages chosen at random, what type of graph would be b
navik [9.2K]

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A bar graph is the best graph to use

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Find the product.<br><br> (23)(−98)(−45)(−1)<br> Enter the correct product in the box.
torisob [31]

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-101,430

Step-by-step explanation:

23 x 98 x 45 x 1 equals 101,430, but the real trick of the question is whether it is positive or negative.

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-2254(-45) forms a positive number (101,430)

101,430(-1) forms a negative number (-101,430)

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My dog, Petey weighs 75 pounds. Last summer he weighed 65 pounds. What percent of his weight did he gain?
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Step-by-step explanation:

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If x&lt;0 and y&gt;0, determine the sign of the real number.​
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