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.
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$\begingroup$ Are you sure about $q>0$ ? what about $y"+y=0$ ? $\endgroup$– ThomasApr 11, 2016 at 16:05
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$\begingroup$ sorry its negative... $\endgroup$– neelkanthApr 11, 2016 at 16:12
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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
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$\begingroup$ i am asking for q is negative $\endgroup$– neelkanthApr 11, 2016 at 16:27
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