Verifying Solution to DE: y' = (1+1/x)y y(1) = e

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Homework Help Overview

The discussion revolves around verifying the solution to a first-order differential equation (DE) given by y' = (1+1/x)y with the initial condition y(1) = e. The original poster expresses uncertainty about their solution after a long period without practice in solving DEs.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to verify their solution y = CXe^x and questions whether their calculations are correct due to a long gap in practice. Some participants suggest checking the solution by substituting it back into the DE.

Discussion Status

The discussion includes attempts to validate the solution, with some participants providing guidance on how to check the work. However, there is no explicit consensus on the correctness of the solution, as the original poster remains uncertain.

Contextual Notes

The original poster mentions a significant time lapse since their last engagement with differential equations, which may influence their confidence in the solution process.

frs2fh
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Hi,
I have a first order equation I've solved to help a friend along in another poblem. But I have not solved a DE in over 10yrs - so I just want to make sure I did it correct.
It an IVP.

y' = (1+1/x)y y(1) = e.

So I come up with y = CXe^x
(C = 1 for IV)
 
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You can easily check it yourself: you have y(x), and can compute y'(x), then plug these into the DE to see if they work.

RGV
 
Thanks Ray,
I did this before I posted and it seemed to work. I'm just afraid if I made a mistake in one direction I made it again in the other. Like I stated, I haven't done this (any integration / derivatives or solving DE) in over a decade. I just want to know if it's correct.
 
It is correct. ehild
 

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