MATH 202 Midterm, Summer 2018

MATH 202 Differential Equations Dr. H. Yamani Midterm Summer 2018 Duration: 80 minutes Problem| 1 2 3 4 5 6 7 8 | Total Pomts | 10 | 12) 12) 2) .1d27) 12) 13 [ 15 |) 108 Scores Name: 7 AUB ID: Problem 1. (10 pts) Find the general solution of the ODE: mw y +8y=0 Problem 2. (12 pts) Solve the following IVP. id =2+ xe0e"[2) GFX bs y(1)= ? Problem 3. (12 pts) Solve the following IVP. (c+ 2)% 4 y-G+2Fy* =0 y(I)=1 Problem 4. (12 pts) Multiply both sides of the ordinary differential equation by an appropriate factor to make it exact. Then solve the IVP. {ey + 3xy” ee + aan 3xy” ay =0 y(t)=1 Problem 5. (12 pts) Show that the differential form in the following integral is exact, then evaluate the integral (2,1,0) | [72 deal ages 2 Jae(Pat este la (0,0) eel Problem 6. (12 points) Let R be the region in the first quadrant bounded by the x-axis, the y-axis and the : Dien. 2 circle x +y =1. Let C be the boundary of R traced counterclockwise. Use Green’s theorem to find the outward flux of the field F = (-” ~ 3x} ~ (y +e “cos xi Problem 7. (15 pts) Use Stokes’ theorem to evaluate the circulation of the field F = — y/+xj+zk around the boundary of the curve x 4+ y = 4 in which the Faree2 : ; plane z = 2 meets the cone z=yx +y traversed counterclockwise when viewed from above. Problem 8 (15 pts) Use the divergence theorem to find the outward flux of the field F = x/ + j+zk across the boundary of the region of the solid which is the entire surface of the upper cap cut from the solid sphere x” +y +27 <25 bythe plane z=3.