Hello I'm studying Airy's equations. In particular I'm interested in the following istance of the equation $v''(x)+xv(x)=0.\tag{1}$
I'm asked to prove that $v$ vanishes infinitely many times on the positive $x$-axis and at most one time on the negative $x$-axis.
How do I answer this question?
I've tried some manipulations, especially connections with the Riccati form. Substituting $u=\frac{v'}{v}\tag{2}$ one arrives to the formula $u'+u^2+x=0,\tag{3}$ however I cannot see if this helps.
Does anybody have any suggestion?
Thanks
-Guido-