Find inverse laplace transform for x(s) = (2)/(s(s+1)^2)

x(t)=

Step-by-step explanation:

The function x(s) = (2)/(s(s+1)^2) can be expressed as partial fractions:

X(s)=

2=A·(s+1)²+B·s·(s+1)+C·s

2=A·(s²+2s+1)+B·(s²+s)+C·s

2=A·s²+2sA+A+B·s²+Bs+C·s

2=s²(A+B)+s(2A+B+C)+A

So we can find the values of A, B and C by solving these equations:

A+B=0 ⇒ 2+B=0 ⇒ B= -2

2A+B+C=0 ⇒ 2·2+(-2)+C=0 ⇒ C= -2

A=2

So X(s) is expressed as:

X(s)=

Using the inverse laplace transform tables we obtain x(t):

ℒ⁻¹{X(s)}=ℒ⁻¹{}

ℒ⁻¹{X(s)}=ℒ⁻¹{}+ℒ⁻¹{}+ℒ⁻¹{}

x(t)=

The answer to your question is    y = 4/3x + 1/3

Step-by-step explanation:

Data

Point A = (2, 3)

Point B = (5, 7)

Process

1.- Calculate the slope

x1 = 2    y1 = 3

x2 = 5    y2 = 7

m = (y2 - y1)/(x2 - x1)

- Substitution

  m = (7 - 3)/(5 - 2)

- Slope

  m = 4/3

2.- Find the equation of the line

     y - y1 = m(x - x1)

     y - 3 = 4/3(x - 2)

     y - 3 = 4/3x - 8/3

     y = 4/3x - 8/3 + 3

     y = 4/3x - 8/3 + 9/3

     y = 4/3x + 1/3