e r t (r 3 − 3 r 2 + 2 r) = 0 r 3 − 3 r 2 + 2 r = 0 r (r 2 − 3 r + 2) = 0 r (r − 1) (r − 2) = 0 \begin{align*} e^{rt}(r^3 -3 r^2 +2 r) &= 0\\ r^3 -3 r^2 + 2r &= 0\\ r(r^2 -3 r + 2) &= 0\\ r(r - 1)(r - 2) &= 0
ASK AN EXPERT. Math Advanced Math Q&A Library Determine the values of r for which the given differential equation has solutions of the form y=e^rt. 1.) y' + 2y=0 answer: r=-2 2.) y -y =0