URI/Spring 2004

Instructor: Prof. M. Kulenović

**Maple Project**

Kingston, 2/18/2004

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/m244sp04/m244sp04hp.html*

**1. **Consider the Bernoulli differential equation:

**(a) **Find the general solution of
this equation by using dsolve command.

(b) Use dsolve
command to find the particular solutions of this equation that satisfies the
initial conditions

Plot the obtained solutions along with the direction field.

**(c) **
Use** Maple **to perform the substitution
and transform the initial equation into linear differential equation.

**2. (a)
**Use Maple to find a solution of the
initial value problem

(b) Plot the obtained solutions along with two more solutions that satisfy the initial conditions

and

**3. (a) **Use Abel's formula

and Maple to find a second linearly independent solution of the following differential equation with the given solution:

(b) Use dsolve command to find the particular solution of this equation that satisfies the initial conditions

and

(c) Plot the obtained solutions along with the direction field.

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