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-