MATH 202 Exam 1, Spring 2007

American University of Beirut MATH 202 Differential Equations Spring 2007 quiz # 1 1. Integrate f(x, y) = (x + y2)/ √ 1 + x2 along the curve C : y = x2 2 from (1, 1/2) to (0, 0) 2. Find the counterclockwise circulation and outward flux of the field F(x, y) = xyi+y2j around and across the boundary of the region enclosed by the curves y = x2 and y = x in the first quadrant 3. Integrate the function H(x, y, z) = yz over the part of the sphere x2 + y2 + z2 = 4 that lies above the cone z = √ x2 + y2 4. Use an appropriate parametrization of the cone z = √ x2 + y2 , 0 ≤ z ≤ 1, to evaluate the surface integral ∫ ∫ S y2dσ 5. Solve the IVP: y′(1 + x2) + xy = 0 , y(0) = 1 6. Solve the IVP: xy′ + 3y = x2 , y(1) = 2/5