Homework-1-f11-solution

# Homework-1-f11-solution - AMS 361: Applied Calculus IV...

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Homework 1 Assignment Date: Thursday (09/08/2011) Collection Date: Thursday (09/15/2011) Grade: Each problem is worth 10 points (Problem 1-1) Verify by substitution that the given functions are solutions of the given differential equation. Primes denote derivatives with respect to x. ! !! + 25 ! = 0 ; ! ! = cos 5 ! , ! ! = sin 5 ! Solution i) ! ! = !"# 5 ! , ! ! ! = 5 !"# 5 ! , ! ! !! = 25 !"# 5 ! ! ! !! + 25 ! ! = 25 !"# 5 ! + 25 !"# 5 ! = 0 ii) ! ! = !"# 5 ! , ! ! ! = 5 !"# 5 ! , ! ! !! = 25 !"# 5 ! ! ! !! + 25 ! ! = 25 !"# 5 ! + 25 !"# 5 ! = 0 (Problem 1-2) 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. ! ! + ! ! ! ! = ! ; ! ( ! ) = !"#\$ ( ! ! ) , ! ( ! ) = ! Solution ! 0 = !"# ! 0 ! = 7 ! = 7 ! ( ! ) = 7 !"# ( ! ! ) , ! ! ! = 3

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## This note was uploaded on 11/14/2011 for the course AMS 361 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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Homework-1-f11-solution - AMS 361: Applied Calculus IV...

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