Sometimes we come across a differential equation that has a second derivative in it, it should look something like .

In this case, we set to be equal to . What happens in this case is due to the properties of the derivative of we get a quadratic equation in terms of , which is very easy to solve:

The exponential can never be zero, so our only solutions, if they exist, are the solutions of the quadratic equation

There are three cases, depending on the determinant of this equation, :