# MATH 244/1

URI/Spring 2005

Instructor: Prof. M. Kulenović

Maple Project 2
Due date: May 3, 2005

Kingston, 4/21/2005

The objective of this project is to use Maple's symbolic manipulation capabilities to solve certain 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 method of Laplace transform implemented in Maple:
y'' + 4 y' - 5 y =  x + 2 ex + x sin(2x)
y(0) = 1, y'(0) = -1.
(b) Find the solution of this equation by using dsolve command.

2. Compute the first twenty terms of the power series solution Σ axn about the initial point for the following initial value problem for Legendre's equation:

(1 - x2 ) y'' - 2 x y' + 12 y = 0.
(a) Find the recurrence relation satisfied by an .

(b) Plot this approximate solution together with the exact solution obtained by applying dsolve command on the interval (-1,1). Use initial condition y(0) = 1, y'(0) = -1.