- #1
kasse
- 384
- 1
Homework Statement
Find a differential eq. y''+ay'+by=0 with this basis: exp(-1-i)x , exp(-1+i)x
2. The attempt at a solution
I see from this that the solutions of the characteristic eq. is two complex conjugates, and that a^2-4b=-4.
Substitution gives me the eq. -2i-a+ai+b=0, and combining these two gives me
a=(1/2) v (1/2)-i
Then I calcutale b when a=(1/2)
b=(17/16)
So that the eq. is
y''+0.5y'+(17/16)y=0
Looks quite nice, but when I transform the bases (exp(-x)*sinx and exp(-x)*cosx) and substitute, it proves not to be correct.
What's my mistake?