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T-3y 2y-8t-5) (4)+110Ja)=O

Question

Use the Laplace transform to find the solution to the given initial value problem. 

Please refer to attached image.

T-3y 2y-8t-5) (4)
+
1
10
Ja)=O
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T-3y 2y-8t-5) (4) + 1 10 Ja)=O

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check_circleAnswer
Step 1

Consider the given initial value problem:

1
y "+3y+2y=8(t-5)+0)
y(0)0, y'(0)
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1 y "+3y+2y=8(t-5)+0) y(0)0, y'(0)

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Step 2

Now, take Laplace transform and apply the following formulae:

L(y"s2y-sy(0)y'(0)
L(y')sYy(0)
L(y) Y
e~Cs
L{u(}=
L{5(t-c=e Cs
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L(y"s2y-sy(0)y'(0) L(y')sYy(0) L(y) Y e~Cs L{u(}= L{5(t-c=e Cs

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Step 3

Therefore, take Laplace tran...

L(y*+3y+2y)=[5/-3)+400
L(y*)+3(y')2()=L[8(1-5)]+z{40(0)}
(32y-sy(0)-y0)+3(sY-y(
0)+27=<
-5s e-10s
S
help_outline

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L(y*+3y+2y)=[5/-3)+400 L(y*)+3(y')2()=L[8(1-5)]+z{40(0)} (32y-sy(0)-y0)+3(sY-y( 0)+27=< -5s e-10s S

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