Question

Use the Laplace transform to solve the following IVP y′′ +2y′ +2y=δ(t−5) ,y(0)=1,y′(0)=2, where δ(t) is...

Use the Laplace transform to solve the following IVP

y′′ +2y′ +2y=δ(t−5) ,y(0)=1,y′(0)=2,

where δ(t) is the Dirac delta function.

Math   Advanced-Math   
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Homework Answers

Answer #1

Taking the Laplace on the LHS,

We know,

So the equation becomes,

Substituting the initial values,

y'(0)=2 and y(0)=1,

Laplace of RHS,

Now,

So,

By splitting,

where, H is the Heaviside step function and

So,

thus,

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