Consider the ordinary differential equation y" + P(x)y' + Q(x)y = 0 where P and Q are smooth functions. Let y1 and y2 be any two solutions of the ODE. Let W(x) be the corresponding Wronskian. Then which of the following is always true?
1
If y1 and y2 are linearly dependent then ∃ x1, x2 such that W(x1) = 0 and W(x2) ≠ 0
2
If y1 and y2 are linearly independent then W(x) = 0 ∀ x
3
If y1 and y2 are linearly dependent then W(x) ≠ 0 ∀ x
4
If y1 and y2 are linearly independent then W(x) ≠ 0 ∀ x