In 112, use the Laplace transform to solve the given differential equation subject to

Chapter 4, Problem 3

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QUESTION:

In Problems 1–12, use the Laplace transform to solve the given differential equation subject to the indicated initial conditions.

\(y^{\prime \prime}+y=\delta(t-2 \pi)\), y(0)=0, \(y^{\prime}(0)=1\)

Questions & Answers

QUESTION:

In Problems 1–12, use the Laplace transform to solve the given differential equation subject to the indicated initial conditions.

\(y^{\prime \prime}+y=\delta(t-2 \pi)\), y(0)=0, \(y^{\prime}(0)=1\)

ANSWER:

Step 1 of 2

Given differential equation is

With initial condition

Taking the Laplace transformation in the both sides of the given equation followed by the given initial conditions, it follows,

Here,

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