- #1
Rijad Hadzic
- 321
- 20
Homework Statement
Find the general solution of the second order DE.
[itex] y'' + 9y = 0 [/itex]
Homework Equations
The Attempt at a Solution
Problem is straight forward I just don't get why my answer is different than the books.
So you get
[itex] m^2 + 9 = 0 [/itex]
[itex] m = 3i [/itex] and [itex] m = -3i [/itex]
so the general solution would be:
[itex] c_1e^{3ix} + c_2e^{-3ix} = y [/itex]
my book gives me
[itex] e^{i\theta} = cos(\theta) + isin(\theta) [/itex]
from there I get
[itex] e^{iβx} = cos(βx) + isin(βx) [/itex]
[itex] e^{i-βx} = cos(βx) - isin(βx) [/itex]
I have
[itex] e^{i3x} = cos(3x) + isin(3x) [/itex]
[itex] e^{i-3x} = cos(3x) - isin(3x) [/itex]
so I get [itex] y = c_1cos(3x) + c_1isin(3x) + c_2cos(3x) -c_2isin(3x) [/itex]
but my book gives me
[itex] y = c_1cos(3x) + c_2sin(3x) [/itex]
I feel like my answer is still valid for some reason.. I just don't know how they got their answer from my answer. I used the correct identity..