Homework-1-Solution

# Homework-1-Solution - AMS 361 Applied Calculus IV(DE&...

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Unformatted text preview: AMS 361: Applied Calculus IV (DE & BVP) Homework 1 Assignment Date: Collection Date: Wednesday (09/09/2009) Wednesday (09/16/2009) 8:20AM Grade: Each problem is worth 10 points. Problem 1-1 (Prob 4, P. 8) : Verify by substitution that the given functions are solutions of the given differential equation. Primes denote derivatives with respect to x. 9; , ; 3 ; 9 ; 3 ; 9 9 9 Problem 1-2 (Prob 24, P. 8): Verify that y(x) satisfies the given differential equation and then determine a value of the constant c so that y(x) satisfies the given initial condition. 3 ; , 1 17 3 3 3 3 3 3 3 ; 1 1 1 17 1 17 10 17 17 Problem 1-3 (Prob 8, P. 16): Find a function y = f ( x) satisfying the given differential equation and the prescribed initial condition. 10 ; 0 0 1 1 1 0 0 10 1 0 10 Problem 1-4 (Prob 13, P.16): Find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x(0) and the initial velocity v0 = v(0) . 3, 7, 4 3 2 3 2 3 2 4 4 2 3 7 7 7 7 7 4 2 7 Problem 1-5 (Deng Book. 20 points for this problem): Find the position function x(t) of a moving particle with the given acceleration a(t), initial position x0 = x(0) and the initial velocity v0 = v(0) . Discuss the four cases for 1, 2, 3 and above. 1 , 0, 0 1 1 1 1 ln 1 1 ln 1 0 0 2 1 1 1 1 1 1 0 3 1 1 2 2 1 1 1 1 2 1 2 1 2 3 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 ...
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