## Wronskian and Second Order Differential Equations

1. The problem statement, all variables and given/known data

Given a second order differential equation:

y'' + P(x)y' + Q(x)y = 0

If y1(x) and y2(x) are linearly independent solutions of the DE, what form does Abel's Equation give for W(y1(x), y2(x))? If we assume that one solution y1(x) is known, what first order DE results from a reduction of order using y1(x)?

3. The attempt at a solution

I know that Abel's Equation gives the form of

W(y1(x), y2(x)) = C$$e^{\int}$$P(x)dx

Where C is a constant

But how would you use an unknown y1(x) to do a reduction of order on the equation?
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 Recognitions: Science Advisor This PDF explains it. http://www.ux1.eiu.edu/~wrgreen2/research/Abel.pdf See the bottom of page 1.