# Tutorial: Euler's Method

This tutorial will show you how to implement the method you have used in class for estimating the solution to a differential equation with an initial condition. This technique is known as Euler's Method. (You may or may not have mentioned the name in class; the name is pronounced "oil-er".)

At each stage of Euler's method, you estimate the y value of the unknown function at the next step using the derivative and the previous y and t values. The basic formula is

y(x+h) = (approximately) y(x) + h y'(x)

## Step One: Determine h and Create a t Column

Given a differential equation, you must determine your step size h. (In 2015, your step size will usually be given to you and it will usually be 1.)

Suppose for example we want to estimate the differential equation y' = y – 2t, with initial condition y(1) = 5 using a step size of = 1 on the interval from 1 to 5. We can then create a column for t values going from 1 to 5 in steps of 1, as shown below:

 A B C 1 t values y values y' values 2 1 3 2 4 3 5 4 6 5

Next, we are ready to fill in y values and y' values for the first row.