...............................
You have the joint density of Y1 and Y2.
Let W=Y1 and find the joint density of W and U.
(That's calc3, jacobians.)
Then integrate out the unnecessary rv W.
And start showing your work here.
The other one is calc1
$\displaystyle f_U(u)=f_Y(y)\biggl|{dy\over du}\biggr|$