Proof of Single Zero Between Consecutive Zeros of y1 & y2

[dismo]

Supose y1 and y2 are a fundamental set of solutions to a second order ODE on the interval
-infinity<t<infinity.
How can I show that there is one and only one zero of y1 between consecutive zeros of y2.

I really don't even know how to egin approaching this problem. Any direction would be greatly appreciated.

 

[moe_3_moe]

only one zero of y1 between consecutive zeros of y2? what do you mean by this statement?

 

[dismo]

I believe that I mean if y1(x)=0 and y1(z)=0 then y2(a) must be equal to zero with x<a<z.

In other words, y1 and y2 must alternate zeros as t varies.