- Question 1 You Are Given A Homogeneous System Of First Order Linear Differential Equations And Two Vector Valued Functio 1 (36.69 KiB) Viewed 34 times
Question 1 You are given a homogeneous system of first-order linear differential equations and two vector valued functions (1) and (2) *-(-2)x: x1)-(3), x2) a. Show that the given functions are solutions of the given system of differential equations. Make sure you can do this on your own. b. Show that XC7Xi!!+ cyx is also a solution of the given system for any values of c, and cz. Make sure you can do this on your own. Show that the given functions form a fundamental set of solutions of the given system. Make sure you can do this on your own. d. Find the solution of the given system that satisfies the initial condition x(0) - (1, 2) e. Find WIX)x)). Show that the Wronskian, W = WXx?), found in part (e) is a solution of Abel's equation: W' - (P116) + Pzz(t/W. Make sure you can do this on your own. None of the answers Part loi me – 12.4.0-(3) Parte) The answer is 2 10 me - 12.2.1) Part I)) - 1/ 21/2x). PartGel The answer is 2 -31 pal Partid x) - 1/ 5.6/5). 5 5 pl So Purtle The answer is 5e Partid vir) - 1/ 5s/5) cost - sint 2cost-3 sint Pantel The anweis-5.