Why is \(y\) squared?

Calculus Level 4

Consider the differential equation \[\frac{dy}{dx}=\frac{\sqrt{x^{2}+y^{2}}-x}{y}\]

Given that \(y(0)=4\), if the equation \(y(x)=0\) has exactly one negative (real) root \(\beta\), find the value of \(\beta\).

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