What are some interesting nonlinear differential equations

Linear & non-linear DGL

Would you like to get to know the difference between linear and non-linear differential equations and what the linear differential equations with constant coefficients are all about? Then you are exactly right here!

  • Difference between non-linear and linear differential equations
    in the text
  • Examples of nonlinear and linear differential equation
    in the text
  • Linear differential equation with constant coefficients - an important special case
    in the text

Difference between non-linear and linear differential equations

Let's start with the linear differential equations. A DGL is called linear if it can be represented in the following form:

The derivatives are multiplied by coefficients and summed. The coefficients can depend on x. If you cannot represent the DGL in this way and y or one of its derivatives is in a non-linear function, it is called non-linear.

Examples of nonlinear and linear differential equations

Next, let's look at two examples:

The first equation is a linear differential equation. In the second equation you can see that: . is thus a non-linear coefficient.

Let's look at another equation:

This is a nonlinear differential equation, because here y is the argument of the nonlinear cosine function, so it is in the cosine itself.

Linear differential equation with constant coefficients - an important special case

In the case of linear differential equations with constant coefficients, the coefficients depend not from from.

Here, too, an example is helpful to better understand the subject.

The coefficient = cos (3) does not depend on x and it follows:

Now you have also learned the difference between linear and nonlinear differential equations and know what linear differential equations with constant coefficients are.