Prof. M. Kulenović
Due date: May 3, 2005
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:
Solve the following initial value problem by the
method of Laplace transform implemented in Maple:
y'' + 4 y' -
5 y = x2
+ 2 ex + x sin(2x)
solution of this equation by using dsolve
y(0) = 1, y'(0) = -1.
2. Compute the first twenty terms of the power
series solution Σ an xn about the
initial point for the following initial value problem for Legendre's
(1 - x2
) y'' - 2 x y' + 12 y
Find the recurrence relation satisfied by an .
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.