Hello experts! As we know that there are 3 different general solutions of an ordinary differential equation depends on that what type of roots we've gotten in the solution, listed below. 1) y(t)=c1em1t+c2em2t 2) y(t)=c1emt+c2temt 3) y(t)=c1eucos(v)+c2sin(v) Now 1st solution is used when discriminant i.e. D>0, 2nd is used when D=0 and 3rd is used when D<0 But here is a question, y''+6y'+9y=0 By solving we get roots, m1=-3 and m2=-3 While discriminant is -30 & book has used 2nd solution to solve it, if D<0 it must use 3rd solution. How do we choose correct solution? Does solution is according to nature of roots(discriminant) or m1 & m2? Thanks for your contribution.