Diff. eq. solve linear equation

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Homework Help Overview

The discussion revolves around solving a linear differential equation of the form 3xy' + y = 12. Participants are exploring the methods for finding the solution and verifying their approaches.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to solve the differential equation but expresses uncertainty about their solution. Some participants suggest verifying the solution by taking the derivative and discuss the calculation of the integrating factor.

Discussion Status

Participants are engaged in clarifying the steps involved in solving the equation, particularly focusing on the integrating factor. There is an acknowledgment of a potential mistake in the calculation, and guidance has been offered regarding the manipulation of the integrating factor.

Contextual Notes

There is an emphasis on ensuring the correct application of logarithmic properties in the context of the integrating factor, which is critical for the solution process. The original poster's confidence in their solution is noted as a point of discussion.

Jtechguy21
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Homework Statement



Solve the following differential equations.

3xy'+y=12

Homework Equations



I believe this is a linear equation problem. So I believed to have solved it, however I am not sure if I have done so correctly.

The Attempt at a Solution


20140301_115639_zps4db21c0a.jpg
 
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If you're not sure, take the derivative and you can verify it from the equation given. The only mistake I see is in calculating your integrating factor:

When you have [itex]e^{\frac{1}{3}lnx}[/itex], you have to move the 1/3 into the exponent on the [itex]lnx[/itex] before you cancel the e and the ln.
 
jackarms said:
If you're not sure, take the derivative and you can verify it from the equation given. The only mistake I see is in calculating your integrating factor:

When you have [itex]e^{\frac{1}{3}lnx}[/itex], you have to move the 1/3 into the exponent on the [itex]lnx[/itex] before you cancel the e and the ln.

thank you for the advice.
I see what you mean. so when the e and the ln cancel out, i should be left over with x^(1/3) as my integrating factor correct?
 
Yes, that looks right. That should give you the right answer.
 

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