Differential equation separated variables

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Homework Help Overview

The discussion revolves around a separable differential equation, with the original poster questioning the correctness of their solution and the possibility of further simplification of the final equation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster seeks validation of their solution and inquires about the potential to calculate a specific variable, V, from their final equation. They also express curiosity about the simplification of similar equations encountered in other exercises.

Discussion Status

Some participants have noted issues with the original poster's solution, pointing out specific errors in the equation. Guidance has been offered regarding the nature of separable differential equations, indicating that further simplification may not be feasible.

Contextual Notes

The discussion includes references to pending approval for attachments, which may be affecting the ability of participants to provide assistance.

esmeco
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Homework Statement



I solved this equation and I was wondering if it's correctly solved...Also, I have one question: In my equation,at the very end, is it possible to calculate the value of V?I have solved other exercises where the final equation was,for example: y + ln[y - 1] = ex + C . Is it possible to simplificate it more?

Homework Equations



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The Attempt at a Solution



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Attachments

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Anyone help?
 
esmeco said:
Anyone help?

I think the reason that no one has helped is that the attachment is still pending approval. You may have to wait a while for it to be approved.
 
You have a couple of missing negatives: at one point [itex]-(1-\frac{1}{v}[/itex] becomes [itex]-1-\frac{1}{v}[/itex]. I would recommend that you rewrite -(1- v) as v- 1.

In this case, no it is not possible to simplify it any more. That's typical separable differential equations- you cannot generally solve for one variable as a function of the other.
 

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