Assignment 16, Spring 2013
Due at 3 PM Friday May 10th
1. For each of the following systems, draw a phase portrait illustrating the behavior of the solutions, using the phase
plane plotter that can be found at the class web page. Be sure to
Assignment 9, Spring 2013
1. Consider the matrix
Due at 3 PM Wednesday, April 24th
(a) Find the eigenvalues. The characteristic equation cant be (easily) factored, so use the quadratic formula. You
should get complex conjugate eigenvalu
Assignment 10, Spring 2013
Due at 3 PM Monday, April 29th
n(n 1) an xn2 .
an xn we get y =
Example 1: When we take the second derivative of the series y =
(Make sure you see how this is obtained!) Make a change of the index variable n to
Assignment 14, Spring 2013
Due at 3 PM Wednesday, May 8th
1. Determine whether x = 0 is an ordinary point (O), regular singular point (RS) or singular point that is not regular
(SNR) for each of the following equations.
(a) 8x2 y + 10xy + (x 1)y
Solving Non-homogeneous Systems
To solve x = Ax + f , x(0) = c:
1) Solve the homogeneous equation x = Ax to get the homogeneous solution xh .
2) Use either undetermined coecients or variation of parameters to nd the particular solutio
Not to turn in - do for Wednesday, May 22nd
Assignment 21, Spring 2013
The nal answers to Exercises 2 and 3 are given below. Ill post the full solutions by the evening of 2/21.
1. Write the ODE y (5) 2y (4) 6y (3) + 3y y + 2y = 3 sin 2t as a syst
Assignment 18, Spring 2013
Due at 3 PM Thursday May 16th
1. Use the Laplace transform to solve the initial value problem y + 4y + 8y = sin 5t, y (0) = 1, y (0) = 2. Many
of you were a bit careless with grouping around the transform of the rst der
Assignment 17, Spring 2013
Due at 3 PM Monday May 13th
For each system given, do each of the following.
(a) Use Wolfram Alpha to nd the eigenvalues and eigenvectors.
(b) Draw the phase portrait using only the eigenvalues and eigenvectors. Then ch
Assignment 15, Spring 2013
1. Solve the system x =
Due at 3 PM Thursday May 9th
x. Give your solution as two separate equations.
2. In this exercise you will plot what we will call trajectories or solutions curves for the solution to t