General Solution to Differential Equation?

[jake2]

Problem Statement

Find the general solution to ty'-4y=(t^6)*(e^t)

Solution Attempt

I added the 4y over and divided by t

y'=[(t^6)(e^t)+4y] / t

I am not sure where to go from here. I'm pretty sure that separation of variables won't work, because I don't think that I can separate the 4y from t.

Now I think I should have just divided through by t and then used integrating factors with \mu=e^(-4ln|t|)=t^-4

Is this correct? Thanks for your help!

EDIT: I've found the solution... It did seem like using integrating factors worked the best. The answer is

y = [(te^t)-(e^t)+c] / (t^-4)

 

[Dick]

I think using that integrating factor is a great idea. Can you finish from there?

 

[jake2]

Yup already finished. The problem got much simpler as things began to cancel. I love it when problems work out nicely. Thanks (:

I think the main thing that hung me up was changing gears from studying how to solve differential equations using Laplace Transforms back to using integrating factors.