Consider the differential equation $$y^{''}+q(x)y=0,q(x)<0$$ where $q(x)$ is a continuous function. Let $y$ be a nontrivial solution of ODE. How to prove that $y,y^{'}$ are strictly monotone functions? Please help me. Thanks in advance.
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$\begingroup$ Are you sure about $q>0$ ? what about $y"+y=0$ ? $\endgroup$– ThomasApr 11, 2016 at 16:05

$\begingroup$ sorry its negative... $\endgroup$– neelkanthApr 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. $\endgroup$– Christian RemlingApr 11, 2016 at 16:24

$\begingroup$ i am asking for q is negative $\endgroup$– neelkanthApr 11, 2016 at 16:27
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