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

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

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To solve the differential equation \((x^2 + xy)dy = (x^2 + y^2)dx\) and show that it is homogeneous, we will follow these steps: ### Step 1: Check Homogeneity To check if the differential equation is homogeneous, we replace \(x\) with \(tx\) and \(y\) with \(ty\) in the equation. The left-hand side becomes: \[ (tx)^2 + (tx)(ty) = t^2x^2 + t^2xy = t^2(x^2 + xy) ...
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