MA 265 Midterm: ERG_MA265_test_2 Spring 2015
Document Summary
Egr 265, math tools for engineering problem solving. 6y + 9y = 0, y(0) = 1, y (0) = 4. Solve the initial value problem y + y . 2y = 5, y(0) = 0, y (0) = 0. Find the general solution of y + 4y = cos x + sin x. A mass of 5 kilograms stretches an undamped spring by 25 centimeters. Assume here that the positive x-direction is oriented downwards. (d) find the rst time t > 0 at which the mass returns to the equilibrium position. Suppose that a damping force is added to the spring-mass system in problem 4 which is proportional to the instantaneous velocity with damping coe cient kg/sec. Problem 6 (12 points) (a) find the partial derivatives fx and fy of the function f (x, y) = x3y3 + x2 + y2 (b) find the second order partial derivative gxy of g(x, y) = ex.
