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?