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# hw1 - Math 205 Spring 2011 B Dodson Text Goode-Annin 3rd...

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Math 205, Spring 2011 B. Dodson Text - Goode-Annin, 3rd edt. Office hours: M,F: 2:20-3:30, Tue: 11:30-12:30 and by appt. email: [email protected]

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2 1. Course Info 2. Homework 1: Chapter 1, Sections 1, 2, 3, 4, 5, 6 Due Monday, Jan 24th
Chapter 1: Intro, Slope Fields, verify solution (Monday, 1/17) 1.4, 1.5: Separable DE, Population/logistic growth (start 1.6; Wednesday, 1/19) 1.6 Linear Equations (Friday, 1/21

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4 Problem 1: Verify that the function y = c 1 x is a solution of y = y 2 x Solution: Compute y and check. y = c 1 ( 1 2 ) x 1 2 . y 2 x = c 1 x 2 x = c 1 ( 1 2 ) x ( x ) 2 = c 1 ( 1 2 ) 1 x = y .
Problem 2: Determine all values r so y = e rx is a solution to y ′′ 4 y + 3 y = 0 .

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6 Linear DE, Main Step: to solve linear DE dy dx + p ( x ) y = q ( x ) multiply by the integral factor f = e integraltext pdx and use d dx ( fy ) = f ( y + py ) on the left to get d dx ( fy ) = fq. Problem: Solve dy dx + 2 x (1 x 2 ) y = 4 x, 1 x 1 . Solution:
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hw1 - Math 205 Spring 2011 B Dodson Text Goode-Annin 3rd...

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