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AP EAPCET (Engineering) Homogeneous DE — practice questions

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To solve a **homogeneous** differential equation of degree 1 (e.g. $dy/dx = f(y/x)$), the standard substitutioSolve the homogeneous DE $x\,dy/dx = x\,\tan(y/x) + y$:Solve $\dfrac{dy}{dx} = \dfrac{y + qrt{x^2 + y^2}}{x}$.Solve $(x^2 - y^2)\,dx + 2xy\,dy = 0$.