# Math Help - Initial Value Problem

1. ## Initial Value Problem

$dy/dt + 0.8ty = 2t$
$y(0) = 9$
This is what I have so far
$dy/dt = 2t - 0.8ty$
$dy/(2- 0.8y) = t dt$
$y/2 - 0.8ln|y| = (t^2)/2 + C$
Solve C:
$C = (9/2)-0.8ln|9|$

Now I'm having trouble isolating Y to get an answer.
Have I taken all the right steps so far, and if so how do I go about isolating Y?
Thank You for any help

2. there are 2 things on this one

1. Since this is a linear DE the whole problem can be solved easier using an integrating factor

is set up perfectly for this

with the integrating factor e^(.4*t^2)

However suppose you want to separate variables

2.first you were ok up to

To integrate the left use u = 2 - 0.8y

you tried to write as dy/2 -dy/(.8y) which is not true

3. Whoa I didn't not even see that it was a integrating factor problem haha thank you very much.