y1(x)=e-8xis a solution to the differential equationD2y-11Dy-152y=0forx∈(-∞,∞). Use the method of reduction of order to find the second solution toD2y-11Dy-152y=0forx∈(-∞,∞).
(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 D2y-11Dy-152y=0 for x∈(-∞,∞) is
y2(x)=