MATH 202 Exam 2, Spring 2010

American University of Beirut MATH 202 Differential Equations Spring 2010 quiz # 2 PUT YOUR SECTION’S NUMBER ON YOUR BOOKLET PLEASE: 18 (T 11) 14 (T 12:30) 15 (T 5) 16 (T 9:30) Exercise 1 Find the general solution of the given differential equation (do not find the con- stants) a) y” — 2y' — 38y = (2? + 1)e* b) y!" + 3y" + 4y’ + 12y = e** + cos(2z) c) y®) — 16y) = 32 +14 22-2" + e* cos(3z) Exercise 2 Solve the initial-value problem 4 1 xz’ — — Qry = 3y* , y1)== give the largest interval J on which the solution is defined. Exercise 3 Use an appropriate substitution to solve zy’ = yln(xy) Exercise 4 Solve the DE Moy = y yry 1422 by variation of parameters. Exercise 5 Consider the DE (E): vty! + a3y! —42?y =1 a. Check that y; = 2? is a solution of the associated homogeneous equation. 2 b. Let yg = x*u(z). Show that u satisfies a first order DE, then solve it. c. Give the general solution of (£) on ]0, +00]. (clearly indicates y. and Yp)