TUT0801 QUIZ4

[taojinwe]

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) = C₁e^3t + C₂te^3t

Then we plug in the value y(0) = 0 and y’(0) =2
 y(0) = C₁e^3t + C₂te^3t = 0
        = C₁e⁰ + C₂0e⁰
        C₁= 0
y’(t) = 3C₁e^3t + 3C₂te^3t + C₂e^3t
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) = 2te^3t