URI/Spring 2005

Instructor: Prof. M. Kulenović

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:

y'' + 4 y' -
5 y = x^{2 }
+ 2 e^{x }+ x sin(2x)

y(0) = 1, y'(0) = -1.

y(0) = 1, y'(0) = -1.

**2. **Compute the first twenty terms of the power
series solution Σ a_{n }x^{n} about the
initial point for the following initial value problem for Legendre's
equation:

(1 - x^{2
}) y'' - 2 x y' + 12 y
= 0.

(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.