Consider the differential equation $$y^{''}+q(x)y=0,q(x)<0$$ where $q(x)$ is a continuous function. Let $y$ be a non-trivial solution of ODE. How to prove that $y,y^{'}$ are strictly monotone functions? Please help me. Thanks in advance.

  • $\begingroup$ Are you sure about $q>0$ ? what about $y"+y=0$ ? $\endgroup$
    – Thomas
    Apr 11, 2016 at 16:05
  • $\begingroup$ sorry its negative... $\endgroup$
    – neelkanth
    Apr 11, 2016 at 16:12
  • 2
    $\begingroup$ This is false of course (play around with the solutions to $y''-y=0$, say), but similar statements are correct. However, your question is not really suitable for this site. Please ask at math.stackexchange.com instead. $\endgroup$ Apr 11, 2016 at 16:24
  • $\begingroup$ i am asking for q is negative $\endgroup$
    – neelkanth
    Apr 11, 2016 at 16:27


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