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Chapter 7: Q4RP (page 415)

In Problems 3–10, 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 15-24, solve for Ys , the Laplace transform of the solution ytto the given initial value problem.

y''-3y'+2y=cost;y0=0,y'0=-1

In Problems 1-20, determine the Laplace transform of the given function using Table 7.1 on page 356 and the properties of the transform given in Table 7.2. [Hint: In Problems 12-20, use an appropriate trigonometric identity.]


cosntsinmt,m≠n

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

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

w''-2w'+w=6t-2;w-1=3;w'-1=7

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

y''+5y'+6y=g(t):y(0)=0,y'(0)=2,whereg(t)={0,0⩽t<1,t,1<t<5,1,5<t
See all solutions

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