1. ## diff eqn question

Can anyone give me a 'walk through talk through' of the following problem?

Use the Laplace Transform method to obtain the forced response of the system

y'+2y=v(t)
assuming zero initial conditions and t>=0 for the following cases:

a) v(t)=t

b) v(t)=t^2

c) v(T)=te^-t

Fingers crossed someone can help. I've been wrestling with it for a couple of days now.

2. Originally Posted by boab
Can anyone give me a 'walk through talk through' of the following problem?

Use the Laplace Transform method to obtain the forced response of the system

y'+2y=v(t)
assuming zero initial conditions and t>=0 for the following cases:

a) v(t)=t

b) v(t)=t^2

c) v(T)=te^-t

Fingers crossed someone can help. I've been wrestling with it for a couple of days now.
Where exactly do you get stuck? Perhaps reading this might help.

3. Thanks. I've done most of these now. I've just hit a sticking point with the last one. I've a feeling I've missed something obvious. I've got to...

1/(s+1)^2(s+2)= A/(s+1) + B/(s+1)^2 + C/(s+2)

1= A(s+1)(s+2) + B(s+2) + C(s+1)^2

Let s = -2 Let s = -1

C = 1 B=1

Is this right and how do I find A?

4. Originally Posted by boab
Thanks. I've done most of these now. I've just hit a sticking point with the last one. I've a feeling I've missed something obvious. I've got to...

1/(s+1)^2(s+2)= A/(s+1) + B/(s+1)^2 + C/(s+2)

1= A(s+1)(s+2) + B(s+2) + C(s+1)^2

Let s = -2 Let s = -1

C = 1 B=1

Is this right and how do I find A?
You can substitute another simple value of s, like s = 0:

1 = 2A + 2B + C

And you already know the values of B and C ......

5. I was right then. I had missed something completely obvious!

Thanks