Proof when the non-homogeneity is the Dirac Delta Function

[mario99]

$$P(x)y'' + Q(x)y' + R(x)y = \delta(x - s)$$$$a < x < b$$
I want to prove the following theorem:

$$y'(x_{+}) - y'(x_{-}) = \frac{1}{P(x)}$$
when

$$P(x) \neq 0$$$$y(a) = y(b) = 0$$

Any help would be appreciated.

 

[topsquark]

$$P(x)y'' + Q(x)y' + R(x)y = \delta(x - s)$$$$a < x < b$$
I want to prove the following theorem:

$$y'(x_{+}) - y'(x_{-}) = \frac{1}{P(x)}$$
when

$$P(x) \neq 0$$$$y(a) = y(b) = 0$$

Any help would be appreciated.

You have clearly stated elsewhere that you are not going to post your work on these problems. Until you do, we can't really help you.

-Dan