Need Help with a Dif Eq

[hakett86]

hi there i need help trying to solve:

(e^x) dy/dx = y-ye^x , y(0) = 2

please any hints will help!!!

[OfficeShredder]

Try a separation of variables:

e^x*dy/dx = y(1-e^x)

dy/dx=y(1-e^x)/e^x

dy/y=(1-e^x)/e^x dx

I'm not sure if this is the best way to do it, but it looks solvable this way (integrate both sides from here)

[Jameson]

That's definitely the best way to do it. Break up (1-e^x)/e^x into (1/e^x)-e^x/e^x or more simply e^(-x)-1.

[lozygo]

There are gains for all our losses.
[size=2] There are balms for all our pain:
But when youth, the dream, departs
It takes something from our hearts,
And it never comes again.
We are stronger, and are better,
Under manhood's sterner reign:
Still we feel that something sweet
Followed youth, with flying feet,
And will never come again.
Something beautiful is vanished,
And we sigh for it in vain;
We behold it everywhere,
On the earth, and in the air,
But it never comes again!