Calculate the Laplace transforms of the following from the definition. 1. y = t^2. y = t^3

Question

asked Apr 28, 2020 176k views

1 Answer

TEH EMPRAH · Answer 1 · 2020-05-05T01:34:24+0000

Answer:

1)
L(y)=(2)/(s^(3))

2)
L(y)=(6)/(s^(4))

Explanation:

To find : Calculate the Laplace transforms of the following from the definition ?

Solution :

We know that,

Laplace transforms of
t^n is given by,

L(t^n)=(n!)/(s^(n+1))

1)
y=t^2

Laplace of y,

L(y)=L(t^2) here n=2

L(y)=(2!)/(s^(2+1))

L(y)=(2)/(s^(3))

2)
y=t^3

Laplace of y,

L(y)=L(t^3) here n=3

L(y)=(3!)/(s^(3+1))

L(y)=(3* 2)/(s^(4))

L(y)=(6)/(s^(4))