# MATH
244/1

URI/Spring 2005

Instructor:
Prof. M. Kulenović

**Maple
Project 3**

Due date: May 10, 2005

Kingston, 4/27/2005

The**
**objective of this project is to use *Maple*'s symbolic
manipulation capabilities to solve numerically differential equations
and
to use *Maple*'s graphics capabilities to plot the required
solutions of these equations.

Use *Maple*'s worksheet that
you will find in:

*http://www.math.uri.edu/~kulenm/m244sp05*

**1. **

**(a)
**Solve the following initial value problem by the
standard numerical
method implemented in Maple**:**

y'
= x^{2 }
+ sin(2y)

y(0) = 1.

**(b)
**Plot the
solution of this initial value problem for the step sizes h = 0.01
and h = 0.05
on interval [0,
2].

**2. **

**(a)
**Solve the following initial value problem by the
standard numerical
method implemented in Maple**:**

y'
= sin(x)^{ }
+ y^{3}

y(0) = 1.

**(b)
**Plot the
solution of this initial value problem together with the solution
obtained by using Euler's method for the step size h = 0.01 on
interval [0,
2].