Please help me with the following problems. These i tried solving with the substitution y=ux but ended up stuck somewhere along the way.

1) y' = (y/x) - exp(y/x) y(1)=1

I got as far as an integral involving -e^-u but couldn't recall how to integrate such a function...

2) y' = (-x + 2y)/y y(1)=2

Similarly got stuck at the integral stage.

The following are problems involving integrating factors.

3) y' + ln(x)y = 1 y(1)=1

Whats the integrating factor and how does one proceed?

4) y' + sin(x)y = sin(x) y(0)=2

I got stuck doing the integration by parts necessary to find the general solution.

5) y' + 3y = exp(x) y(0)=1

6) y' + e*y = x y(1)=2

Also there are a couple of problems involving the undetermined coefficient method. I'm completely at a loss as to what that is. If someone could explain it I'd be very grateful and could attempt those questions by myself.

Thanks very much for any help, apologies for not posting in latex format, i tried to make everything clear and legible.