MAT244H1S FINAL ASSIGNMENTDUE TUESDAY APRIL 14 AT 9AMOpen book, open notesExam policies:? You may discuss the problems with your classmates but must write up your solutionsindependently. Credit will be divided equally between identical submissions.? Solve each problem on its own page (or set of pages). After you are done, upload your workfor each problem as a pdf to the corresponding problem on Crowdmark.? You may write your solutions on paper or, if you prefer, on a computer. Should you writeon paper, please scan or take a high quality picture of each page, and combine them into onefile before uploading. The Office Lens application for Android or iOS can combine multiplescanned pages into a single PDF file (but you may use any tool that works for you).? Detail the main steps of your solution (e.g. if you need to compute the eigenvalues ofa matrix A, you should write down its characteristic polynomial). Your reasoning willbe at least as important in our scoring as your final numerical answer. You may receivesubstantial partial credit if your approach is sound but you make an arithmetic error at theend.? You may refer to the textbook, any notes from lecture, and any notes posted on Quercus.12 DUE TUESDAY APRIL 14 AT 9AM1. (1代寫MAT244H1S作業(yè)胆敞、Java編程語言作業(yè)代做着帽、代寫c/c++杂伟，Python作業(yè) 代寫Web開發(fā)|代寫R語言程序0 points) Solve each of the following initial value problems, and express the solution as aexplicit function of t.2. (10 points) For real parameters b and c, consider the equation.Describe, both in terms of inequalities and with a sketch, the region of the bc plane suchthat every solution satisfieslimt→∞y(t) = 0.3. (10 points) Find the general solution to the equationy(4) ? 2y00 + y = cost.4. (20 points) Consider the systemdxdt = x(1 ? x ? y),dydt = y(2 ? x ? y).First determine the critical points. Then for each critical point:(a) Find the corresponding linear system near the critical point.(b) Determine the stability and type of the critical point, and sketch some nearby trajectories.5. (10 points) Let A be a real 4 × 4 matrix and consider the initial value problem(1) = Ax, x(0) = ξ0,where ξ0 ∈ R4 be a vector such that (A ? 3I)3ξ0 = 0 but ξ1 := (A ? 3I)ξ0 6= 0 andξ2 := (A ? 3I)2ξ0 6= 0.(a) Make the change of variable x = e3ty, and derive an equation y0 = By (find B).(b) Solve the initial value problemy0 = By, y(0) = ξ0,representing y in terms of ξ0, ξ1, and ξ2. [Suggestion: use the matrix exponential.](c) Solve the original initial value problem (1) in terms of ξ0, ξ1, and ξ2.轉(zhuǎn)自：http://www.daixie0.com/contents/13/4954.html