Solving Difficult Equations: y = -2x - 2/7 + ce^(-7x)

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Homework Help Overview

The discussion revolves around the equation y = -2x - 2/7 + ce^(-7x), specifically focusing on the form of the term ce^(-7x) and its interpretation in the context of solving differential equations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the form of the term ce^(-7x) versus c/e^(-7x), with some expressing agreement on the need for clarification. There is a suggestion to verify the solution by substituting it back into the differential equation.

Discussion Status

The discussion is exploring different interpretations of the equation's terms. Some participants have offered guidance on checking the solution's validity, but there is no explicit consensus on the correct interpretation of the term in question.

Contextual Notes

There appears to be confusion regarding the compatibility of the last two lines of the solution, indicating potential errors in the previous steps. Participants are encouraged to verify their solutions against the original differential equation.

kyu
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Homework Statement





Homework Equations



i have done till the 2nd final step
how is it possible to get the final answer y = -2x - 2/7 + ce^(-7x)
why is it ce^(-7x) and not c/e^(-7x)?

The Attempt at a Solution

 

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I agree with you. It should be ##c/e^{-7x}=ce^{7x}##.
 
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kyu said:

Homework Statement





Homework Equations



i have done till the 2nd final step
how is it possible to get the final answer y = -2x - 2/7 + ce^(-7x)
why is it ce^(-7x) and not c/e^(-7x)?

The Attempt at a Solution


You are correct.
 
While this was a quite blatant error where the last two lines were not compatible with each other. If you are in doubt, you can always insert the solution into the differential equation and check that it actually solves it.
 

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