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Chapter 7: Q17RP (page 350)

Determine the inverse Laplace transform of the given function.

e-2s(4s+2)(s-1)(s+2)

Short Answer

Expert verified

The solution isL-1e-2s(4s+2)(s-1)(s+2)=(2et-2+2e-2t+4)u(t-2)

Step by step solution

01

Step 1:Given Information.

The given function value in s domain is .e鈭�2s(4s+2)(s鈭�1)(s+2)

02

Determining the inverse Laplace transform

Make partial fraction of the given function, as:

4s+2(s鈭�1)(s+2)=As鈭�1+Bs+2

On comparing the two sides of the above equation we get:

4s+2=A(s+2)+B(s-1)

On comparing the coefficients with s=鈭�1,2respectively we get

A=2B=2

Thus, the partial fractions are obtained as:

4s+2(s鈭�1)(s+2)=2s鈭�1+2s+2

We now have

L鈭�1e鈭�2s(4s+2)(s鈭�1)(s+2)=L鈭�12e鈭�2ss鈭�1+L鈭�12e鈭�2ss+2=2et鈭�2u(t鈭�2)+2e鈭�2(t鈭�2)u(t鈭�2)=(2et鈭�2+2e鈭�2t+4)u(t鈭�2)

Hence, the required inverse Laplace transform is.

L-1e-2s(4s+2)(s-1)(s+2)=2et-2+2e-2t+4u(t-2)

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Most popular questions from this chapter

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'-2y=2x(1)=1

x'+x-y'=t2+2t-1y(1)=0

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

10.y''-4y=4t-8e-2t;y(0)=0,y'(0)=5

Determine the inverse Laplace transform of the given function.

2s2+3s-1(s+1)2(s+2)

solve the given initial value problem using the method of Laplace transforms.

y''+2y'+2y=u(t-2蟺)--u(t-4蟺);y(0)=1,y'(0)=1

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