Differential Equations exam - Intro Differential Equations | MATH 2214, Exams of Differential Equations

Download Differential Equations exam - Intro Differential Equations | MATH 2214 and more Exams Differential Equations in PDF only on Docsity! Mate- ve cass Wed~ km w~;w¥ Sad awa LAST NAME (Print clearly) ... , beet tees eee eeseeeeeeeeteeeeeeeeeeeseeeaes FIRST NAME (Print clearly) . OE nee eens Student Identification Number Pt ee nee ene es MATH 2214Introduction to Differential Equations Exam 3, Novernber 17, 2006 Total of exam [30] INSTRUCTIONS e This exam consists out of three questions. © e No caleulators, cell phones or other clectronic devices are allowed on your person. ¢ Show all your workings in order to receive partial credit. \ A \ 4 (CEN: « You may not use red ink to write this exam. « All exams are to be done without any assistance from anyone else. Your work here is at all times governed by the Virginia ‘Tech Honor Code. QUESTION 1 {17] Consider the initial value problem it vit) ~2yn(é) bye(t}, (0) = 1 walt) —5yr(t)t dye), — ya(0) = 3. 1.1 Write the given system in the form y'(t) = Ay(t), y(to) = yo. Bb JEL, ehh 1.2 Find the eigenvalues and associated eigenvectors of the cocflicient matrix, A. ‘ Ve yor fat oo ce, (eRraA FF * [3 4 | det (A 28) Maa] Pe aa f Aaah WYO > [2 s \ Jee) ~ Gy, 4%, =O to = ox, ~ 4 . fig ded —~_ - ek wreetor esto h/ VF Ls [= eteo aith As 4 wv zaabearoe LEST KX N29 Wy ke, os =f } dens asssciat tf 1 |, eigenvector ssscioted with Ae-(, eo \ —( 1.3 Give the of solution to the geen of differential equations. see oe |s |tae aie ~ A 14 Find the particular solution of the initial value problem. Foy = ce evel! (=[3] nk ey 40a © Bah 1.5 Write down a matrix T for which T-!AT = D where D is a diagonal matrix. Also, write down what D is. (You neod not compute Ty wu ria Q? Oe ee eM ote | ce | a