Wronskian and Second Order Differential Equations

metgt4

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[tex]e^{\int}[/tex]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?

Stephen Tashi

This PDF explains it. http://www.ux1.eiu.edu/~wrgreen2/research/Abel.pdf
See the bottom of page 1.