Diff. eq. solve linear equation

[Jtechguy21]

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

 

[jackarms]

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

 

[Jtechguy21]

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 $e^{\frac{1}{3}lnx}$, you have to move the 1/3 into the exponent on the $lnx$ 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?

 

[jackarms]

Yes, that looks right. That should give you the right answer.