Find the integral curves of the given vector field. The vector field is as follows: 
$X_{(x,y)} = x \dfrac{\partial}{\partial x} - y \dfrac{\partial}{\partial y} = \begin{bmatrix} x \\y \end{bmatrix}$.
I know that to find integral curves, you need to solve a differential equation. So here, I would take a derivative of $X$, but I am not completely sure of what to do. With other integral curve computations, I'm usually given some initial conditions. Tips on how to get started would be very helpful. That's really all I'm asking for here. I can do the rest of the math myself. I'm just struggling setting it up. 

Solve for $x,y$ the equations
$$\dot x=x\\ \dot y=-y$$ and so the integral curve would be $$\alpha(t)=
(x(t),y(t))$$
