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

Show that the differential equation `(x^(3)-3xy^(2))dx=(y^(3)-3x^(2)y)dy` is homogenous and solve it.

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To show that the differential equation \((x^3 - 3xy^2)dx = (y^3 - 3x^2y)dy\) is homogeneous and to solve it, we will follow these steps: ### Step 1: Check if the equation is homogeneous A differential equation is homogeneous if both sides can be expressed as functions of \(x\) and \(y\) of the same degree. 1. Rewrite the equation: \[ (x^3 - 3xy^2)dx - (y^3 - 3x^2y)dy = 0 ...
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