- Be patient. The applet may take a long time to load and start.
- Click inside the text area under
**Equations**. - Type into it the differential equation you want to solve,
for example
`y' = x y^2 - cos(y)` - Press the
**Enter**key.Points to keep in mind:

- The derivative is denoted by an apostrophe
**'**. - The independent variable is normally
*x*, but you can change this by clicking on the choice box after **Independent Variable**. - You can use either
`*`or space for multiplication. For example,`4 x y`and`4*x*y`are both OK. But don't just write`xy`without a space. - Use the caret
`^`(on the 6 key) for exponents. - Use
`exp(x)`instead of`e^x`. - Functions such as
`sin`and`exp`need parentheses around their arguments. - There is no distinction between upper and lower case.

- The derivative is denoted by an apostrophe
- After you enter a differential equation, an
input area for the dependent variable (here
*y*) will appear under **Initial Values**. You can enter into it the initial value*y*_{0}of that variable. - The initial and final values of the independent variable are set in the
**Initial X**and**Final X**boxes on the left side. Thus if your initial condition was at*x*= 1 and you wanted the solution at_{0}*x*= 3 you would enter 1 for_{f}**Initial X**and 3 for**Final X**. - Click the left mouse button on
**Euler**, and a list of numerical methods drops down. Click on the one you want to use. - At
**Number of steps**enter the number*N*of steps of the method to perform. Thus the step size will be *dx = (x*_{f}- x_{0})/N. - When everything is set up, click the
**Go**button. This will find an approximation to the solution of the initial value problem, and show you the final values of the variables under**Final Values**. - To see the table of saved values, click the
**Results**button. During the solution process, values of the variables are recorded at**Number of saved values**values of the independent variable (in addition to the initial values). This number can never be more than**Number of steps**. If it divides**Number of steps**evenly, the values are recorded at equal intervals. - It is possible to enter more than one equation, and they don't all have to be
differential equations. For example, if you want to compare the values of
*y*to some known function of*x*, say*x*^{2}, you could add a new equation (by clicking the**Insert equation**button), and enter the equation`z = y - x^2`Then when you click

**Go**and**Results**, the applet will compute and show the values of*z*together with those of*x*and*y*. Up to three columns of data can be shown in the**Results**window, representing any three variables. Click on the names of the variables there to choose which variables to show, and in what order. Generally, not all the data are visible at one time: use the scroll bars to see the rest.