Question

How to find out if linear differential equation is homogeneous?

Answer 1

Answer:

The general form of a linear differential equation is always of the form:

Let us assume the order of the equation is 2. Then,

⇒ y'' + p(x) y' + q(x) y = r(x)

This is an example of a linear differential equation of order 2.

In simple terms, if the coefficient of derivatives or functions used in the equation are constants like 2, 3, etc., then the given equation is a linear equation.

Now if r(x) in the above mentioned example is equal to zero (0), then the given equation is called as Homogeneous equation.

If r(x) ≠ 0, then it is called as Non-Homogeneous equation.

Some examples of Linear Homogeneous differential equations:

• y' + 2.sin(x). y = 0
• y''' + 3x². y'' + y' = 0