# Help finding the function

1. Nov 29, 2011

### yamdizzle

I have

(θ$_{1}$-θ$_{2}$)*exp(r*t) + r* Y = dY/dt

How can I find Y?
I tried to reverse the f ' g +g' f but I keep getting an extra term

Thanks

2. Nov 29, 2011

### LCKurtz

Write it as
$$y' - ry = (\theta_1-\theta_2)e^{rt}$$ Multiply both sides by e-rt and you should have an exact derivative on the left side.

3. Nov 29, 2011

### yamdizzle

Couldn't quite get it? What do you mean by exact derivative?

so what is y?

4. Nov 29, 2011

### LCKurtz

Show us what happened when you followed my advice. The left side should look like the derivative of a product. What did you get?

5. Nov 29, 2011

### yamdizzle

so we have:

exp(-r*t) y' - exp(-r*t) r y = theta1 - theta2

I assume you mean
f = exp(-r*t)
g = y

but I'm not sure how to place thetas

so I think y will have a exp(r*t) in it but not sure about the rest.

Last edited: Nov 29, 2011
6. Nov 29, 2011

### LCKurtz

Yes, so the left side is (e-rty)' so your equation is: $$(e^{-rt}y)'=\theta_1-\theta_2$$ I assume the thetas are constant. So what do you get when you integrate both sides with respect to t and solve for y?

7. Nov 30, 2011

Yep, got it.

Thanks