Mik We Work F15 MATH 33 X CHome Chegg C webwork2mathumassedu

Mik We Work F15 MATH 33 X CHome Chegg C webwork2.math.umass.edu MATH 331 4/Homework2.2/6/?effectiveUser-mturkmani&displayMode; images&showoldAnswers; 1&* O E App SPIRE Log Mood at UM A... M Log in to UM Am M mturkmani@umass.... My Wiley PLUS wil We Work F15 MA. Home Chegg.com https engineering Logged in as mturkmani Log O A A MATHEMATICAL ASSOCIATION OF AMERICA MAIN MENU webwork 5 math 331 4 homework2.2 6 Courses Homework Sets Homework 2.2: Problem 6 Homework 2.2 Problem 6 Prev Up Next Password/Email (1 pt) (a) Find the general solution to y\" 6y\' 9y 0. n your answer, use C1 and C2 to denote arbitrary constants and T he independent variable. Enter C1 as c Grades and Co as c2 help (equations) Problems Problem 1 2 and y\'(0) 0 y (0 b) Find the solution that satisfies the initial conditions Problem 2 help (equations) Problem 3 Note: You can earn partial credit on this problem. Problem 4 Problem 5 Preview Answers Submit Answers Problem 6 You have attempted this problem 0 times. You have unlimited attempts remaining. Display options Email instructor View equations a o images O Math Math Jax O LaTeXMathML 8:57 PM 4) ENG Search the web and Windows 10/16/2015

Solution

y = e^(3x) - xe^(3x)

first you solve the homogeneous equation:
y\'\' - 6y\' + 9y = 0
by assuming y = e^(rx)
substitution gives you:
r^2 - 6r + 9 = 0
(r-3)*(r-3) = 0
so you have a double root of r =3
This means the homogeneous solution is:
y = A*e^(3x) + B*x*e^(3x)

Then you use the initial value and the boundary condition
y(0) = A + B = 2
y\' = 3*A*e^(3x) + B[3x*e^(3x) + e^(3x)]
y\'(0) = 3*A + B = 0

Solving the system
A+B = 2
3A + B = 0
Gives A = -1, B = 3