Part (i) I guess you'll just have to find y'(x) that should be .
So y'(x) = .
now find 2yx. You know what y is, so that shouldn't be hard.
Add both and simplify to get 0.
This proves that the given function is a solution.
Part (ii) Next, use the given conditions, y=0.5 when x = 0.
Just plug the values for x and y in the given equation for y. That should be pretty easy