The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). y'' − 12y' + 36y = 0; y1 = e6x

Given , assume a second solution of the form , with derivatives

With , you have and .

Substitute these into the ODE and you get

Now substitute , so that and you have a linear first-order ODE:

But is already accounted for, so the second fundamental solution to the ODE is .

35/2 is it i think maybe