5 Problems with Solutions on Differential Equations - Exam 1 | MA 3253, Exams of Mathematics

Download 5 Problems with Solutions on Differential Equations - Exam 1 | MA 3253 and more Exams Mathematics in PDF only on Docsity!

MATII 3253 SPRING 2014 TEST 1 the right “As a Missi all times. I ippi State Univ conduct myself %, ll not lie, cheat, or steal, nor will | accept the actions c Show your work to have a full credit. 1.(6) Determine a region in the xy-plane for which the differential ec 5 xi yg dy (1— y)'? = = cos(x*) ax has a unique solution passing through each point in the region. 2.(6) Consider the autonomous differential equation dy 3 = —4y dn y Find the critical numbers and phase portrait of the equation. By hand. sketch typical solutions in the region in the zy plane determined by the graph of the equilibrium solutions. 3.(75) Solve a. (32?y? — y? + cosx)da + (22%y — 8ay? + ye*)dy =0, y(0)=1 Cx. b. lt +y=1 Veneacc da c. cosa de — (e¥ + 1)(sing +1) dy=0 septs ole, , dy _ ytde | d. da Sy how, dy 2x+1 gt+1lo\, Ale 2 pa = Ibernoul\\: eet a 7 © 4, (7) Find an integrating factor for y dx + (2ry — ~*¥) dy =0 and then solve the equation. 5.( 6) Ared wine is brought up from he wine cellar, which a cool 10°C, and left to breath in a room of temperature 23°C. If it takes 10 min for the wine to reach 15°C, when will the temperature of the wine reach 18°C?