Solving for du/dt: tdt= \frac{2+2u-du}{1+u}

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Homework Help Overview

The discussion revolves around manipulating a differential equation involving the variable \( u \) and its derivative with respect to \( t \). The original poster presents an equation and seeks clarification on its form and potential next steps in solving it.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions whether their manipulation of the equation is appropriate or if an alternative approach should be considered. Another participant suggests factoring the expression to simplify the equation, highlighting a common term that could aid in separation.

Discussion Status

Participants are actively engaging with the problem, with one providing a suggestion for factoring to facilitate further steps. There is acknowledgment of understanding from the original poster, indicating that the discussion is moving in a productive direction.

Contextual Notes

Participants are working within the constraints of a homework assignment, focusing on the manipulation of the equation without providing complete solutions.

suspenc3
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[tex]\frac{du}{dt}=2+2u+t+tu[/tex]

I manipulated it to:[tex]-tdt= \frac{2+2u-du}{1+u}[/tex]

Should it be in this form? or try something else?
 
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suspenc3 said:
[tex]\frac{du}{dt}=2+2u+t+tu[/tex]


Note that 2 + 2u + t + tu, can be factored.

First factor the 2 from the first two terms leaving
2(1+u) + t + tu
Then factor the t from the last two terms and you have
2(1+u) + t(1+u)
Now you should notice that you have a common term of (1+u) which can be factored out leaving
(2+t)(1+u)
And now you can easily separate this equation.
 
Riight, I see it now, Thanks
 
suspenc3 said:
Riight, I see it now, Thanks

No problem glad I could help.
 

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