Find the general solution to y′′′+12y′′+61y′=0. In your answer, use c1,c2 and c3 to denote arbitrary constants and x the independent variable. Enter the solution as an equation y=?.

Answer 1

We assume a solution of the form y = e^rx. Plugging this in gives r³ + 12r² + 61r = 0. We can cancel a factor of r and note that r = 0 is one solution. r² + 12r + 61 = 0 ⇒ r = -6 ± 5i. Thus y = c₁ + c₂e^-(6-5i)x + c₃e^-(6+5i)x.