1. ## Hard differential equation

y''+6y'+9y = e^(-3x)/X^3

I don't know what to do when b^2-4ac is zero. When I do the Wronskien matrix I can't solve for C1 and C2 cause my y1 and y2 are the same:

x^2 + 6x + 9 = 0

delta = 0

Y(x) = c1e^-3x + c2e^-3x

Can anyone help?

2. Originally Posted by Provoke
y''+6y'+9y = e^(-3x)/X^3

I don't know what to do when b^2-4ac is zero. When I do the Wronskien matrix I can't solve for C1 and C2 cause my y1 and y2 are the same:

x^2 + 6x + 9 = 0

delta = 0

Y(x) = c1e^-3x + c2e^-3x

Can anyone help?
$y(x)=c_1e^{-3x}+c_2{\color{red}x}e^{-3x}$, since you have repeated roots.

3. Originally Posted by Chris L T521
$y(x)=c_1e^{-3x}+c_2{\color{red}x}e^{-3x}$, since you have repeated roots.
Ahhh! Tickle me with a feather lol, thanks alot man!