Dependent solutions of differential equation

Oct 2012
257
19
israel
Hi,
Let y"+p(x)y'+q(x)y=0 be a second order homogeneous linear equation,where p(x) and q(x) are continuous functions on the infinite interval (0,infinity).
y1(x) and y2(x) are two solutions such that their wronskian is zero at the point x=1.
Can we conclude that y1(x) and y2(x) are dependent in the entire interval (0,infinity) ,or only on every subinterval (a,b) containing x=1?

Thank's in advance