Engr 213 midterm 2a 2009

Engr 213 midterm 2a 2009

• 1.
  Concordia University March 20, 2009 Applied Ordinary Differential Equations ENGR 213 - Section J Prof. Alina Stancu Exam II (A) Directions: You have 60 minutes to solve the following 4 problems. You may use an admis- sible calculator. No cell phones are allowed during the exam. (1) (8 points) Determine whether the functions f1 (x) = x, f2 (x) = x2 , f3 (x) = 4x − 3x2 are linearly dependent or linearly independent on the interval (0, ∞). (2) (15 points) Solve the initial value problem y − 2y + 2y = 2x − 2, y(0) = 2, y (0) = 0. (3) (12 points) Solve the differential equation y + y = csc2 x. (4) (5 points) Find a general solution of the differential equation xy + 2y = 0. 1 1 Useful Formulas: sec x = , csc x = , sec u du = ln | sec u + tan u| + C, cos x sin x csc u du = ln | csc u − cot u| + C. 1