How should I integrate this differential equation?

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Discussion Overview

The discussion revolves around the integration of a specific differential equation, dQ/dt = 10 - 10Q/(500 - 5t). Participants explore various methods for solving the equation, including integrating factors and separation of variables, while also debating the linearity of the equation in terms of the variable Q.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asks for help in integrating the differential equation.
  • Another participant suggests the use of "integrating factors" as a potential method for solving the equation.
  • It is noted by some that the equation is linear in Q, implying familiarity with Ordinary Differential Equations of Order 1.
  • A participant mentions that variables can be separated for the homogeneous equation and that Lagrange's method could be applied to the non-homogeneous part.
  • There is a discussion about the linearity of the equation, with one participant asserting it can be expressed in a linear form, while another clarifies a misunderstanding regarding the placement of terms.
  • Participants express differing opinions on the complexity of the methods discussed, with some finding integrating factors cumbersome.

Areas of Agreement / Disagreement

Participants generally agree on the methods available for solving the differential equation, but there is disagreement regarding the linearity of the equation in Q, with some asserting it is linear and others suggesting it is not.

Contextual Notes

There are unresolved points regarding the interpretation of the equation's linearity and the implications of the methods discussed, particularly concerning the placement of terms in the equation.

irony of truth
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How should I integrate this differential equation?

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

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

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

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

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

[tex] <br /> \frac{dQ}{dt} + \frac{10}{500 - 5t} \cdot Q = 10<br /> [/tex]

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

Daniel.
 

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