# Ordinary Differential Equations

1. Mar 7, 2010

### sassie

1. The problem statement, all variables and given/known data

Give the general solution to the IVP

L[y]=y'+(sint)y=$$\delta$$(t-$$\tau$$)
y(0)=0

For all t>0 by placing a jump condition on y(t) and solving the differential equation for t<$$\tau$$ and t>$$\tau$$

2. Relevant equations

3. The attempt at a solution

I'm plenty sure I can get the general solution to the problem, but I do not at all know how to get the "jump condition" as it wasn't explained in lectures or in the textbook. Your help is very much appreciated.

Last edited: Mar 7, 2010
2. Mar 7, 2010

### vela

Staff Emeritus
Integrate the differential equation from $\tau-\varepsilon$ to $\tau+\varepsilon$ and take the limit as $\varepsilon\rightarrow 0$. That will give you a result that tells you how big the discontinuity in y(t) is at $t=\tau$.

3. Mar 7, 2010

### sassie

So what would we get when we integrate $$\delta$$(t-$$\tau$$)? would it be 1?

4. Mar 7, 2010

### vela

Staff Emeritus
Yes, because the interval of integration includes the point $t=\tau$.