Consider the second order linear equation(adsbygoogle = window.adsbygoogle || []).push({});

z" + c(t)z = 0

Where c(t) is a continuous real-valued function of a real variable.

(a) Show that every (nontrivial) solution of this equation is non-oscillatory if c(t) < (1 - epsilon)/(4t^2) for t>=1, where epsilon > 0 is a real number.

(b)Show that every (nontrivial) solution of this equation is oscillatory if c(t) > (1+epsilon)/(4t^2) for t>=1, where epsilon > 0 is a real number.

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# Second order differential equation problem

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