Hi all i need some help with understanding auxillary equation based on boundary values
An example was:
y" + 2y' + y
with y(0) = 1, y(1) = 3
thus putting it into the auxillary equation and finding the roots:
r1 = r2 = -1
putting it into the formula gave
y = C1e^(-x) + C2xe^(-x) note that C1 is C with subscript one and so on :3
Heres the part i dont get. In my book it says
since y(0) = 1 we have 1 = y(0) = C1
Further, as y(1) = 3 we have
3 = y(1) = e^(-1) + C2e^(-1)
So C2 = 3e - 1 and therefore:
y = e^(-x) + (3e-1)xe
Can someone help me with this (could you also explain why C1 disappeared)?
Your contribution is much appreciated.