Question

Among the following equations, the one which is not a homogeneous differential equation is .

• A. $\frac{dy}{dx}=\frac{y}{x}$
• B. $\frac{dy}{dx}=\frac{x^3+y^3}{2x{y}^2}$
• C. $\frac{dy}{dx}=x^2+y^2$
• D. $\frac{dy}{dx}=\frac{y^{2}sin\left(x/y\right)}{xy}$

Answer 1

The correct option is C $\frac{dy}{dx}=x^2+y^2$

$\frac{dy}{dx}=f(x,y)$ is a homogeneous differential equation only when f(x,y) is a homogeneous function of degree 0. In this case, $f(x,y)=x^2+y^2$ is homogeneous function of degree 2.