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Homework Assignment #1 Fall 2013 - MATH308 due August 30, 2013 at the beginning of class Topics covered : equations y 0 = ay + b, where a and b are constant, and separable equations (corresponds to sections 1.2, 2.2 in the textbook). You do not need to use calculator for this assignment. 1. Assume that the velocity v of the falling object satisfies the following differential equation: v 0 (t) = 9.8 − v 30 (1) (a) Find a number ve such that v(t) ≡ ve is a solution of equation (1) (in other words find the equilibrium solution of (1)). (b) Solve the equation (1) with initial condition v(0) = 98. What is the limit of this solution when t → +∞? How this limiting velocity is related to your answer in the item (a)? (c) Find the time that must elapse for the object to reach item (b). 2 of the limiting velocity found in the 3 (d) How far does the object fall in the time found in the item (c)? 2. Solve the following differential equations (find the general solutions): (a) (1 + x2 )1/3 y 0 + xy 2 = 0 (b) dx + x4 sin ydy = 0; 1