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Chapter 7: Q3RP (page 415)

In Problems 3鈥�10, determine the Laplace transform of the given function.t2e-9t

Short Answer

Expert verified

L{t2e-9t}(s)=2(s+9)3

Step by step solution

01

Step 1:Given Information.

The given function is .t2e鈭�9t

02

Determining the Laplace transform:

Using the Laplace transform definition,L{tneat}=n!(s-a)n+1we get

L{t2e-9t}=2!(s+9)3=2(s+9)3

03

Determining the Result

Thus, the required Laplace transform is .L{t2e-9t}(s)=2(s+9)3

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Most popular questions from this chapter

Determine the inverse Laplace transform of the given function.


6(s-1)4.

In Problems 1鈥�19, use the method of Laplace transforms to solve the given initial value problem. Here x鈥�, y鈥�, etc., denotes differentiation with respect to t; so does the symbol D.

x''+y=1;x(0)=1,x'(0)=1x+y''=-1;y(0)=1,y'(0)=-1

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

3.y''+6y'+9y=0;y0=-1,y'0=6

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x''+2y'=-x;鈥夆赌夆赌�x(0)=2,鈥夆赌夆赌�x'(0)=-7,-3x''+2y''=3x-4y;鈥夆赌夆赌�y(0)=4,鈥夆赌夆赌�y'(0)=-9

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

y''+5y'+6y=tu(t-2)y(0)=0y'(0)=1
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