Question
Asked Jul 10, 2019

Use Laplace Transforms 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_circleExpert Solution
Step 1

Consider the given initial value problem:

1
y (0)=0, y"(0)=
y"+3y'+2y=8(t-5)+0()
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1 y (0)=0, y"(0)= y"+3y'+2y=8(t-5)+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')sY-y(0)
L(y) Y
e cs
L{u(}=
eCS
L{5(t-c=e Cs
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L(y"s2y-sy(0)y'(0) L(y')sY-y(0) L(y) Y e cs L{u(}= eCS 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')+3L (y')+2(y)=L[S1-5)]+L{10)}
2y-sy(0)-y10))+3(s7-y(0)+2
-5s e-10s
+2Y
S
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L(y*+3y+2y)=[5/-3)+400 L(y')+3L (y')+2(y)=L[S1-5)]+L{10)} 2y-sy(0)-y10))+3(s7-y(0)+2 -5s e-10s +2Y S

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