General Solutions

Question 1

The roots are real and distinct?

Answer 1

y = Ae^r₁x + Be^r₂x

Question 2

The roots are real and equal?

Answer 2

y = Ae^rx + Bxe^rx

Question 3

The roots are imaginary and distinct?

α +- βi

Answer 3

y = e^αx(A cosβx + Bsinβx)