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Chapter 7: Q7.3-1E (page 365)

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.]


t2+etsin2t

Short Answer

Expert verified

Lt2+etsin2t=2s3+2(s-1)2+4

Step by step solution

01

Find the Laplace transform of the given function

Consider the function t2+etsin2t

Since Laf1+bf2=aLf1+bLf2, Lt2+etsin2t=Lt2+Letsin2t.

Since Ltn=n!sn+1and Leatsinbt=b(s-a)2+b2, Lt2+Letsin2t=2!s2+1+2(s-1)2+22

Therefore, Lt2+etsin2t=2!s2+1+2(s-1)2+22because Lt2+etsin2t=Lt2+Letsin2t.

Hence,Lt2+etsin2t=2s3+2(s-1)2+4.

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Most popular questions from this chapter

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.]

cosntcosmt,m鈮�n

In Problems 1-10, determine the inverse Laplace transform of the given function.

3s-152s2-4s+10

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

2y''-y'-2y=0

In Problems 1 and 2, use the definition of the Laplace transform to determine L{f}.

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