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It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system,
x?' = A x?
Here the eigenvalues of the matrix A are complex. By using complex eigenvalues we are going to have similar problem that we had back while we were looking at second order differential equations. We need our solutions to only have real numbers in them, though as our solutions to systems are of the form,
x?1 = ?h elt
We are going to contain complex numbers come in our solution from both the eigenvector and the eigenvalue. Getting rid of the complex numbers now will be same to how we did this back in the second order differential equation case, although will include a little more work this time around. It's simple to see how to do it in an example.
Application Practice Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Sav
sin(x)+cos(x)
(x+y+1)dy/dx=1
1. Four different written driving tests are administered by a city. One of these tests is selected at random for each applicant for a drivers license. If a group of 2 women and 4 m
Area with Polar Coordinates In this part we are going to look at areas enclosed via polar curves. Note also that we said "enclosed by" in place of "under" as we usually have
Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1)
solving sums
Example of Circles - Common Polar Coordinate Graphs Example: Graph r = 7, r = 4 cos θ, and r = -7 sin θ on similar axis system. Solution The very first one is a circle
Find out if the following series is convergent or divergent. Solution There really is not very much to these problems another than calculating the limit and then usin
larry spends 3/4 hours twice a day walking and playing with his dog. He spends 1/6 hours twice a day feeding his dog. how much time does larry spend on his dog each day?
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