2nd Order Diff Eqn. (complex roots)

[aznkid310]

Homework Statement

Prove that if y1 and y2 have maxima or minima at the same point in I, then they cannot be a fundamental set of solutions on that interval.

Homework Equations

Do I take the wronskian (determinant of y1, y1', y2, y2')? What would that tell me?

The Attempt at a Solution

 

[HallsofIvy]

1) What is the Wronskian?

2) Why do you mention it here? What does the Wronskian have to do with differential equations?

 

[aznkid310]

The wronskian is a determinant that tells us whether a set of functions is linearly independent or not right? How does that relate to maxima/minima?

 

[HallsofIvy]

If y1 and y2 have maxima or minima at the same point, what are y1' and y2' there? What is the Wronskian at that point?