Science:Math Exam Resources/Courses/MATH152/April 2011/Question B 02 (b)
• QA 1 • QA 2 • QA 3 • QA 4 • QA 5 • QA 6 • QA 7 • QA 8 • QA 9 • QA 10 • QA 11 • QA 12 • QA 13 • QA 14 • QA 15 • QA 16 • QA 17 • QA 18 • QA 19 • QA 20 • QA 21 • QA 22 • QA 23 • QA 24 • QA 25 • QA 26 • QA 27 • QA 28 • QA 29 • QA 30 • QB 1(a) • QB 1(b) • QB 1(c) • QB 2(a) • QB 2(b) • QB 3(a) • QB 3(b) • QB 3(c) • QB 4(a) • QB 4(b) • QB 4(c) • QB 4(d) • QB 5(a) • QB 5(b) • QB 5(c) • QB 6(a) • QB 6(b) • QB 6(c) • QB 6(d) • QB 6(e) •
Question B 02 (b) 

Consider the differential equation system where A has eigenvalues and with corresponding eigenvectors Find the solution that matches the initial conditions 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

How can we use our solution from part(a) and the initial conditions to find the true particular solution? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Recall from part (a) that we figured out that the general solution was With the initial condition we can find the constants and for this particular problem. Plugging in the initial condition we get, Therefore we conclude that, which has solution, and . Therefore the solution to this problem with initial condition is 