Question about second order differential equation

I have this problem, which says: If the graph of one solution for the equation is tangent to the x axis in some point of an interval [a,b], then that solution must be identically zero. Why?

I've tried to do something with the general expression for the solution.

So I've considered y'(x)=0, because y(x) must be tangent to the x axis.

So, I don't know what to do next. I think this is not the right way.

I think I got it.

y(x_0)=0, it touches the x axis

y'(x_0)=0

Thats all?