Solve DE: (y-1)e^y = [(x^2+1)^(3/2)]/3 + C

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Discussion Overview

The discussion revolves around solving the differential equation given by (y-1)e^y = [(x^2+1)^(3/2)]/3 + C. Participants explore methods for finding y and discuss integration steps related to the equation.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the differential equation and expresses difficulty in solving for y.
  • Another participant critiques the integration of the right-hand side (RHS) and suggests that the integration was not performed correctly.
  • A later reply acknowledges a mistake in the initial posting of the derivative and thanks the participants for their input.
  • One participant suggests isolating x in the problem, noting that this would lead to a solution with a plus or minus sign.

Areas of Agreement / Disagreement

There is no consensus on how to proceed with solving the differential equation, as participants have differing views on the integration and the approach to isolating variables.

Contextual Notes

Participants have not fully resolved the integration steps, and there are indications of missing assumptions regarding the manipulation of the equation.

Growl
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Given that y' = [x(x^2+1)^1/2]/ye^y
How do you find solve the differential equation?
I got through some parts but have hard time solving for y when i got
(y-1)e^y = [(x^2+1)^(3/2)]/3 + C

Thanks a lot :)
 
Last edited:
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It looks like you did a bit of a botch job on integrating the RHS.

[tex]\int x^3 + xdx = x^4/4 + x^2/2[/tex]

I don't think you can really go much farther than you have.

EDIT: It looks right now. I would probably just hand it in as is, because I don't see a way to solve that
 
Last edited:
My bad, it's actually y' = [x(x^2+1)^1/2]/ye^y, ;), posted the problem up wrong...

Thanks anyway!
 
if you want to give your professor something, you can isolate x in that problem, although you'll have a plus or minus in the solution..
 

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