Suppose that u(t) is a solution to
y'' + p(t)y' + q(t)y = 0
Suppose a second solution has the form
y(t) = m(t)u(t)
where m(t) is an unknown function of t. Derive a first order linear differential equation for m'(t).
Suppose y(t) = e^(2t). Use the method above to find a second solution to this equation.
The Attempt at a Solution
y = m*u
=> m = y/u
=> m' = (y'/u) - (y/(u^2))*u'
There isn't anything in my book or in my class notes that describes the technique to be used here. Does anyone have any suggestions on how to get started?