Homework-1-Solution

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

Ask a homework question - tutors are online