Question

(4s²-2s-3)+(5s²+7s-6)

​

Answer 1

Respuesta

Example 1. Determine the inverse Laplace transform of the given function.

(a) F(s) = 2

s

3

.

SOLUTION. L

−1

2

s

3

 

= L

−1

2!

s

3

 

= t

2

(b) F(s) = 2

s

2+4 .

SOLUTION. L

−1

2

s

2+4  

= L

−1

2

s

2+22

 

= sin 2t.

(c) F(s) = s+1

s

2+2s+10 .

SOLUTION. L

−1

s+1

s

2+2s+10  

= L

−1

n

s+1

(s+1)2+9o

= L

−1

n

s+1

(s+1)2+32

o

= e−t

cos 3t.

Theorem 1. (linearity of the inverse transform) Assume that L

−1{F}, L

−1{F1},

and L

−1{F2} exist and are continuous on [0, ∞) and c is any constant. Then

L

−1

{F1 + F2} = L

−1

{F1} + L

−1

{F2}

L

−1

{cF} = cL

−1

{F}.

Example 2. Determine L

−1

n

3

(2s+5)3 +

2s+16

s

2+4s+13 +

3

s

2+4s+8o

.

Explicación paso a paso: