Assume that $p(x)<0$ for all real numbers and y(x) is a solution of the DE $$y'+p(x)y=0$$ that is not identically zero. I need to prove that y can cross the x axis at most once.
I don't understand the answer below, any other help, please?
Rough idea: between two consecutive zeroes of $y$, $y'$ must vanish. But $y'=-p(x)y(x)$, which has constant sign between consecutives zeroes of $y$.