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Show that the differential equation is `x(dy)/(dx)-y=sqrt(x^(2)+y^(2))`, is homogenous and solve it.

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To solve the differential equation \( x \frac{dy}{dx} - y = \sqrt{x^2 + y^2} \), we will first show that it is homogeneous and then solve it step by step. ### Step 1: Rewrite the equation We start by rewriting the given equation: \[ x \frac{dy}{dx} = y + \sqrt{x^2 + y^2} \] ...
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