Quick question on differential equation

[WannabeNewton]

Homework Statement

If the metric for (x^{i}) is
G = \begin{bmatrix} (x^{1})<br /> &amp; 0 \\ <br /> 0 &amp; 1<br /> \end{bmatrix}

a) write the differential equations of the geodesics in terms of the dependent variables u = (x^{1})^{2} and v = x^{2}; (b) integrate these equations and eliminate the arc - length parameter from the solution.

The Attempt at a Solution

I wrote out the geodesic equations in full and when I looked over the Christoffel symbols and all of the terms having them vanished for x^2 and one of them remained for x^1. The book's simple statement of the answer gives
d^2v / ds^2 = d^2u / ds^2 = 0
and I have no idea how they came to that. Sorry if this is very trivial and I am just being an idiot.

I am also confused for part (b). Does the question want me to integrate with respect to ds or multiply out ds and then integrate? Also how many constants would I need to add after integrating and where? Thank you in advance.