There is Poincare disc model with metric $g=4\dfrac{dx^2+dy^2}{(4-x^2-y^2)^2}$ I have to find geodesic lines in this model. I tried with system of differential equation, but it is very complicated. I have:
$ (\frac{x'}{(4-x^2-y^2)^2})' -2x\frac{(x')^2+(y')^2}{(4-x^2-y^2)^3} = 0$
$ (\frac{y'}{(4-x^2-y^2)^2})' -2y\frac{(x')^2+(y')^2}{(4-x^2-y^2)^3} = 0$
Also, I tried polar coordinates, but still nothing