We know that y1(x) = e^{-3x} is a solution to the differential equation D^2y - 15Dy - 54y = 0 for x ∈ (-∑, ∑). Use the method of reduction of order to find the second solution to D^2y - 15Dy - 54y = 0 for x ∈ (-∑, ∑).
(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 - 15Dy - 54y = 0 for x ∈ (-∑, ∑) is y2(x) =