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Show that the differential equation 2x^(...

Show that the differential equation `2x^(2)(dy)/(dx)-2xy+y^(0)=0` is homogeneous and solve it.

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To solve the given differential equation \( 2x^2 \frac{dy}{dx} - 2xy + y^2 = 0 \), we will first show that it is homogeneous and then solve it step by step. ### Step 1: Show that the equation is homogeneous A differential equation is homogeneous if it can be expressed in the form \( \frac{dy}{dx} = f\left(\frac{y}{x}\right) \). Starting with the given equation: \[ ...
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