(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

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# Homework Help: Finding a diff. eq.

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