Question

$\frac{dy}{dx}=x^2+y^2$ is a homogeneous differential equation.

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{dy}{dx}=f(x,y)$ is a homogeneous differential equation only when f(x,y) is a homogeneous function. Also f(x,y) should have its degree = 0.
Now in the given equation, $x^2+y^2$ is a homogeneous function but its degree is 2 not zero. So it’s not a homogeneous differential equation. Please note that homogeneous function and homogeneous differential equations are two different things.