**
Differential
Equations - Math 207**

**O****nline Applications**

**Sect.
1.3/1.4:
Direction Fields and Approximation
of Solutions to IVPs using Euler's Method **This applet allows you
to type in a differential equation of the form y' = f(x,y). It will show
the direction field for a particular window. You can change the point that
is the initial condition for the IVP by typing in a new point or simply dragging
the given point. The solutions are approximated by using Euler's method.
If you would like to see a "smoother" and more accurate solution, enter a
smaller value for the step size h.

**Sect. 1.4:
Approximation
of Solutions to IVPs using Euler's Method** To apply Euler's
Method using this applet, you need to enter the following:

**1)** f(x,y):
From your differential equation y' = f(x,y)
(See the notes on the site for help on entering f(x,y))

**2)** x_{0} and
y_{0}: Initial Conditions

**3) **b: The x-value you want to end with

**4)** n:
The number of intervals/steps

You need to select "Enter" and then clicking on "Run" will advance the approximation by each step until you reach b.