We know that $y_1(x) = e^{-6x}$ is a solution to the differential equation $D^2y - 13Dy - 114y = 0$ for $x \in (-\infty, \infty)$.
Use the method of reduction of order to find the second solution to $D^2y - 13Dy - 114y = 0$ for $x \in (-\infty, \infty)$.
(a) After you reduce the second order equation by making the substitution $w = u'$, you get a first order equation of the form
$w' = f(x, w) =$
Note: Make sure you use a lower case w, (and don't use w(t), it confuses the computer).
(b) A second solution to $D^2y - 13Dy - 114y = 0$ for $x \in (-\infty, \infty)$ is
$y_2(x) =$