Flow Line of this Vector Field

Question

I need to find the flow line of the field $F(x,y,z) = e^y\hat i + x\hat j + xy^2z\hat k$ that passes through the point (2,1,1). The answer is supposed to be in the form $x = f(y), y = y, z = g(y)$. I was wondering if someone could check if my answer was correct, I got $x = \sqrt{2(e^y + 2 - e)}$ and $z = e^\left(1/3\left(y^3 - 1\right)\right)$