# 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.