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## Homework Statement

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

I tried:

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?

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