The method of Problem 20 can be extended to second order equations with variable coefficients. If y1 is a known nonvanishing solution of y′′ + p (t) y′ + q (t) y = 0, show that a second solution y2 satisfies (y2 / y1) ′ = W (y1, y2) / y21, where W (y1, y2) is the Wronskian of y1 and y2. Then use Abel's formula [Eq. (23) of Section 3.2] to determine y2.
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