Mik We Work F15 MATH 33 x CHome Chegg C n webwork2mathumasse

Mik We Work F15 MATH 33 x CHome Chegg C n webwork2.math.umass.edu MATH 331 4/Homework2.2/2/?effectiveUser-mturkmani&displayMode; mages&showoldAnswers; 1&SMS; O E /webwork2/F15 EE App SPIRE Log Th Mood at UM A... M Log in to UM Am M mturkmani@umass.... My Wiley PLUS W We Work F15 MA. CHome l Chegg https://engineering.... WeBWorK Logged in as mturkm ani. Log O A A MATHEMATICAL ASSOCIATION OF AMERICA MAIN MENU webwork f15 math 331 4 homework2.2 2 Courses Homework Sets Homework 2.2: Problem 2 Homework 2.2 Problem 2 Prev Up Next Password/Email (1 pt) Solve the following differential equation: Grades 10 10 at r Answer: y(r) F Problems Problem 1 Preview Answers Submit Answers Problem 2 You have attempted this problem 0 times. Problem 3 You have unlimited attempts remaining. Problem 4 Problem 5 Email instructor Problem 6 Display options View equations as: o images O Math O Math Jax O LaTeXMathML 8:57 PM HE Search the web and Windows ENG 10/16/2015

Solution

Find the general solution by solving the auxiliary equation:
y\'\' - 3y\' - 10y = 0
m² - 3m - 10 = 0
(m + 2)(m - 5) = 0
m + 2 = 0 OR m - 5 = 0
m = -2 OR m = 5
y = C^(5x) + C^(-2x)

Find the particular solution by solving for the constant:
When x = 0, y = 1
C + C = 1
y\' = 5C^(5x) - 2C^(-2x)
When x = 0, y\' = 10
5C - 2C = 10
Solving these equations gives C = 12 / 7, C = -5 / 7.
y = 12^(5x) / 7 - 5^(-2x) / 7
y = 12^(5x) / 7 - 5 / [7^(2x)]