finding the flow of a differential equation

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Solve this differential equation

$$x^{\prime}=\frac{-y}{\sqrt{x^2+y^2}},$$ $$y^{\prime}=\frac{x}{\sqrt{x^2+y^2}}$$ in $A=\{(x,y): x^2+y^2\in[1,4]\}$. Could help me get the general equation for the flow in A?