How should I integrate this differential equation?

In summary, the conversation discusses different methods for integrating a given differential equation, specifically using integrating factors and Lagrange's method. There is also a brief discussion about the linearity of the equation in Q and clarifications are made by Daniel.
  • #1
irony of truth
90
0
How should I integrate this differential equation?

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

I hope someone can help me.
 
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  • #2
Have you learned about "integrating factors" yet?
 
  • #3
Isn't that equation linear in Q?

If you know your Ordinary Differential Equations of Order 1 then there should be no problem. ^^;
 
  • #4
Variables can be separated for the homogenous equation,indeed.And then Lagrange's method would work for the nohomogeneity function.

Daniel.
 
  • #5
dextercioby said:
Variables can be separated for the homogenous equation,indeed.And then Lagrange's method would work for the nohomogeneity function.

Daniel.
That's CUMBERSOME..:wink:
Integrating factor rules! :approve:
 
  • #6
True,when the function in Q (in this case) IS NOT LINEAR...:tongue2:...integrating factor rules...

Daniel.
 
  • #7
Can you explain to me why this equation is not linear in Q? I mean, the equation can be put into the form:

[tex]

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

[/tex]

Which to me looks like it's linear in Q...
 
  • #8
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
oh, i see... I am at fault for misunderstanding :tongue: Sorry ^^;
 
  • #10
I should have placed the (...) b4 the "Q"...There would have made more sense...

Daniel.
 

What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivative. It is used to model many real-world phenomena and is often solved using integration techniques.

Why is it important to integrate a differential equation?

Integrating a differential equation allows us to find an explicit solution for the function being modeled. This can provide valuable insights into the behavior of the system and can be used to make predictions.

What are the steps to integrate a differential equation?

The steps to integrate a differential equation depend on the type of equation and the techniques being used. Generally, the first step is to identify the type of equation (linear, separable, exact, etc.) and then apply the appropriate integration method. This may involve rewriting the equation, using substitution or integration by parts, and solving for the constant of integration.

Are there any common mistakes to watch out for when integrating a differential equation?

Yes, some common mistakes include forgetting to add the constant of integration, misapplying integration techniques, and making algebraic errors. It is important to double-check your work and make sure it is consistent with the original equation.

Can differential equations be solved analytically?

Some differential equations can be solved analytically, meaning an exact solution can be found. However, many equations are too complex to solve analytically and require numerical methods to approximate a solution. It is important to carefully consider the problem and the available techniques when attempting to solve a differential equation.

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