Test1_23F_a_sol

Test I A Fall Semester 2023 MATH 308 Differential Equations Dr. Minchul Kang Texas A&M University | Department of Mathematics | 335B Blocker Building | College Station | TX 77840 | grcorg@tamu.edu Direction □ Do not turn to the next page until you are told to do so. □ Print your name and UIN below as well as on the Scantron form. □ Please turn off all mobile phones, calculators, and other electronic device, and stow those away in your bags. □ Your desk may only contain pens, pencils, erasers, and student IDs during the test. □ In part I (Multiple choice questions), mark your answer on the scantron from using No. 2 pencil. □ In part II (Short answer questions), ensure that your final response is typed clearly and legibly in the provided answer box. You don’t have to show your work. □ In part III (Work out questions), show your work to earn credits for work out problems: merely having final answers does not suffice. □ There are 8 pages in this test set. Name: , UIN: Last Name First Name THE AGGIE HONOR CODE "An Aggie does not lie, cheat, or steal or tolerate those who do.” Signature: Test I A| MATH 308 Differential Equations [1/8]

Part I. Multiple choice (4 points each) Print your answer in the box provided. Problem 1. Find differential equation of the direction fields. A . y ′ = y x * B . y ′ = x y C . y ′ = − y x D . y ′ = − x y E . None of above [Answer] Problem 2. Find the order of x ( y ′′′ ) 2 + x 2 ( y ′′ ) 3 + x 3 ( y ′ ) 4 + x 4 y 5 = 0 A . 2 B . 3 * C . 4 D . 5 [Answer] Problem 3. Which of the following is a separable dif- ferential equation? A . y 2 ln x − x 2 y = xy ′ B . y ln x − xy 2 = xy ′ C . y ln x − x 2 y = xy ′ * D . y ln x − xy + x = xy ′ E . None of above [Answer] Problem 4. Which of followings is an exact differential equation? A . (3 x − 2 y ) dx + (3 y + 2 x ) dy = 0 B . (2 x − 3 y ) dx + (3 x − 2 y ) dy = 0 C . (3 x − 2 y ) dx + (2 y − 3 x ) dy = 0 D . (2 x − 3 y ) dx + (2 y − 3 x ) dy = 0 * E . None of above [Answer] Test I A| MATH 308 Differential Equations [2/8]