Question

Using the Laplace transform, solve the system of initial value problems:

w ′′(t) + y(t) + z(t) = −1

w(t) + y ′′(t) − z(t) = 0

−w ′ (t) − y ′ (t) + z ′′(t) = 0

w(0) = 0, w′ (0) = 1, y(0) = 0, y′ (0) = 0, z(0) = −1, z′ (0) = 1

Answer 1

We have,

(1)

(2)

(3)

Taking laplace transform on both sides of (1) we get,

(4)

Taking laplace transform on both sides of (2) we get,

(5)

Taking laplace transform on both sides of (3) we get,

(6)

Adding (4) and (5) we get,

(7)

Using (7) in (6) we get

(8)

  

Substracting (6) from (4) we get,

  

  (9)

From (7) we get:

[using (9)]

Hope this helps!