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Chapter 7: Q4RP (page 415)

In Problems 3鈥�10, determine the Laplace transform of the given function.e3tsin4t

Short Answer

Expert verified

L{e3tsin4t}(s)=4(s-3)2+16

Step by step solution

01

Step 1:Given Information

The given function is e3tsin4t.

02

Determining the Laplace transform:

Using the Laplace transform definition, L{eatsinbt}(s)=b(s-a)2+b2we get

L{e3tsin4t}(s)=4(s-3)2+42=4(s-3)2+16

03

Determining the Result

Thus, the required Laplace transform is .L{e3tsin4t}(s)=4(s-3)2+16

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Most popular questions from this chapter

In Problems 1-14, solve the given initial value problem using the method of Laplace transforms

y''-7y'+10y=9cost+7sint;y0=5,y'0=-4

In Problems 25 - 32, solve the given initial value problem using the method of Laplace transforms.

y''+2y'+10y=g(t);y(0)=-1,y'(0)=0,whereg(t)={10,0猢�t猢�10,20,10<t<20,0,20<t

In Problems 3-10, determine the Laplace transform of the given function.f(t)=cost,-蟺/2鈮�t鈮�蟺/2and f(t)has period蟺

In Problems 29 - 32, use the method of Laplace transforms to find a general solution to the given differential equation by assuming y(0)=aandy'(0)=ba and b are arbitrary constants.

y''-5y'+6y=-6te2t

solve the given initial value problem using the method of Laplace transforms. Sketch the graph of the solution.y''+y=t--(t--4)u(t--2);y(0)=0,y'(0)=1
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