Which one of the following is a homogeneous differential equation?

Which one of the following is a homogeneous differential equation?
  1. $\frac{d y}{d x}=x^3+(\sin x) y$
  2. $\frac{d y}{d x}=\left(x^3+y^3\right) e^{\frac{x}{y}}+x \sqrt{y}$
  3. $\left(x^2+y^2\right) d x=2 x y d y$
  4. $x \frac{d y}{d x}=y+e^{\frac{x}{y}}$

Solution

$\because$ Degree of each term in the differential equation $\left(x^2+y^2\right) d x=2 x y$ dy is same (equal to 2 ). $\therefore\left(x^2+y^2\right) \mathrm{dx}=2 x y d y$ is a homogeneous differential equation.

Asked in: AP EAMCET 2023 (17 May Shift 1)

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