### Author Topic: TUT0801 QUIZ4  (Read 686 times)

#### taojinwe

• Jr. Member
• Posts: 5
• Karma: 0
##### TUT0801 QUIZ4
« on: October 18, 2019, 10:11:18 PM »
Solve the initial value problem
y’’ - 6y’ + 9y = 0
y(0) = 0
y’(0) =2

Convert the problem into the form r2 - 6r + 9 = 0
(r-3)(r-3)=0
r1 = r2 = 3
Since r1 = r2 , we use the formula
y(t) = C1e3t + C2te3t

Then we plug in the value y(0) = 0 and y’(0) =2
y(0) = C1e3t + C2te3t = 0
= C1e0 + C20e0
C1= 0
y’(t) = 3C1e3t + 3C2te3t + C2e3t
y’(0) = 3C1e0 + 3C20e0 + C2e0 = 2

3C1 + C2 = 2
Since  C1 = 0
Then C2 = 2

Therefore, the solution for this initial value problem is y(t) = 2te3t