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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Second order differential equation problem

**Physics Forums | Science Articles, Homework Help, Discussion**