Question

(a) Find the general solution to y'' - 6y' + 9y = 0. Enter your answer as y = ... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2. y=(c1e^(3x)+c2x*e^(3x)) (b) Find the solution that satisfies the initial conditions y(0) = 6 and y'(0) = 0. 6e^(3x)-18xe^(3x)

Name: (a) Find the general solution to y” - 6y' + 9y = 0. Enter your answer as y = ... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2. y=(c1*e^(3x)+c2*x*e^(3x)) (b) Find the solution that satisfies the initial conditions y(0) = 6 and y'(0) = 0. 6e^(3x)-18*x*e^(3x)
Uploaded: 2022-03-30T01:06:15-08:00
Duration: 5 min 22 s
Channel: Vishal Parmar
Description: (a) Find the general solution to y” - 6y' + 9y = 0. Enter your answer as y = ... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2. y=(c1*e^(3x)+c2*x*e^(3x)) (b) Find the solution that satisfies the initial conditions y(0) = 6 and y'(0) = 0. 6e^(3x)-18*x*e^(3x)

          (a) Find the general solution to y'' - 6y' + 9y = 0. Enter your answer as y = ... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2. y=(c1*e^(3x)+c2*x*e^(3x)) (b) Find the solution that satisfies the initial conditions y(0) = 6 and y'(0) = 0. 6e^(3x)-18*x*e^(3x)

(a) Find the general solution to y” - 6y' + 9y = 0. Enter your answer as y = ... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2. y=(c1*e^(3x)+c2*x*e^(3x)) (b) Find the solution that satisfies the initial conditions y(0) = 6 and y'(0) = 0. 6e^(3x)-18*x*e^(3x)

Added by Damon M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vishal Parmar

03/30/2022

Step 1

** Given differential equation: y'' + 6y' + 9y = 0 Auxiliary equation: R^2 - 6R + 9 = 0 (R - 3)^2 = 0 R = 3 (with multiplicity 2) General solution: y = C1e^(3x) + C2xe^(3x) ** Show more…

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(a) Find the general solution to y'' + 6y' + 9y = 0. Enter your answer as y = C1e^(3x) + C2xe^(3x). (b) Find the solution that satisfies the initial conditions y(0) = 6 and y'(0) = 0. The solution is y = 6e^(3x) - 18xe^(3x).