Homogenous constant coefficient linear differential equations

[kmikias]

Hello
I am kinda confused when it comes to finding a general solution of equation.
Here is the question.

Y^'' + 6Y^' +9Y = 0
Solution
Y^'' + 6Y^' +9Y = 0
I used "x" instead of Lamda...ANYWAY

X^2 + 6X + 9 = 0
FACTOR IT WHICH IS (X+3) (X+3) = 0

X IS EQUAL TO -3.

HERE IS WHERE I GET CONFUSED

WHEN I WRITE THE GENERAL SOLUTION ...DO I SUPPOSE TO WRITE
Y= C₁ e^-3x + C₂ e^-3x

or

Y = C₁ e^-3x

WHICH ONE IS CORRECT?

 

[LCKurtz]

Hello
I am kinda confused when it comes to finding a general solution of equation.
Here is the question.

Y^'' + 6Y^' +9Y = 0
Solution
Y^'' + 6Y^' +9Y = 0
I used "x" instead of Lamda...ANYWAY

X^2 + 6X + 9 = 0
FACTOR IT WHICH IS (X+3) (X+3) = 0

X IS EQUAL TO -3.

HERE IS WHERE I GET CONFUSED

WHEN I WRITE THE GENERAL SOLUTION ...DO I SUPPOSE TO WRITE
Y= C₁ e^-3x + C₂ e^-3x

or

Y = C₁ e^-3x

WHICH ONE IS CORRECT?

Neither is completely correct. A repeated root of r gives solution pair {e^rx,xe^rx}.