How should I integrate this differential equation?

1. Feb 15, 2005

irony of truth

How should I integrate this differential equation?

dQ/dt = 10 - 10Q/(500 - 5t)

I hope someone can help me.

2. Feb 15, 2005

arildno

Have you learnt about "integrating factors" yet?

3. Feb 15, 2005

relinquished™

Isn't that equation linear in Q?

If you know your Ordinary Differential Equations of Order 1 then there should be no problem. ^^;

4. Feb 15, 2005

dextercioby

Variables can be separated for the homogenous equation,indeed.And then Lagrange's method would work for the nohomogeneity function.

Daniel.

5. Feb 15, 2005

arildno

That's CUMBERSOME..
Integrating factor rules!

6. Feb 15, 2005

dextercioby

True,when the function in Q (in this case) IS NOT LINEAR...:tongue2:...integrating factor rules...

Daniel.

7. Feb 15, 2005

relinquished™

Can you explain to me why this equation is not linear in Q? I mean, the equation can be put into the form:

$$\frac{dQ}{dt} + \frac{10}{500 - 5t} \cdot Q = 10$$

Which to me looks like it's linear in Q...

8. Feb 15, 2005

dextercioby

It is,u missunderstood the "(...)" part.It was meant for Q...I would have said "y",but "in this case" it was Q involved...

Daniel.

9. Feb 15, 2005

relinquished™

oh, i see... I am at fault for misunderstanding :tongue: Sorry ^^;

10. Feb 15, 2005

dextercioby

I should have placed the (...) b4 the "Q"...There would have made more sense...

Daniel.