Solutions of a linear, second-order, homogeneous differential equation

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Homework Statement
Show, by means of the Wronskian, that a linear, second-order, homogeneous diffferential equation of the form y''+P(x)y'+Q(x)y=0 cannot have 3 independent solutions.

The attempt at a solution
I tried by constructing a Wronskian of 3 general solutions expecting the wronskian to disappear but it didn't so I'm guessing I've gone about this the wrong way?
 

Answers and Replies

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vela
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Let y1, y2, and y3 be solutions to the differential equation. That means

y1'' + P(x) y1' + Q(x) y1 = 0
y2'' + P(x) y2' + Q(x) y2 = 0
y3'' + P(x) y3' + Q(x) y3 = 0

Try expressing that system of equations in matrix form.
 

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