3.- (a) Show that the given equation is homogeneous. (b) Solve the differential equation. dy/dx = -[(x^2 + y^2)/(x^2 - xy)]
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Step 1
Let's substitute tx and ty into the equation: $$\frac{d(ty)}{d(tx)} = -\frac{(tx)^2 + (ty)^2}{(tx)^2 - (tx)(ty)}$$ Now, let's simplify the equation: $$\frac{t\frac{dy}{dx}}{t} = -\frac{t^2x^2 + t^2y^2}{t^2x^2 - t^2xy}$$ $$\frac{dy}{dx} = -\frac{x^2 + y^2}{x^2 Show more…
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