Let \(p(t)>\alpha >0\) be a smooth function defined for all \(t\). Prove that for any solution of \[ x''+p(t)x'+x=0, \tag {4} \] \(x(t)\to 0\) as \(t\to \infty \).
Question
Math 6410 • ODE
Fall 2019 • Question 3
Question
Fall 2019 • Question 3
Let \(p(t)>\alpha >0\) be a smooth function defined for all \(t\). Prove that for any solution of \[ x''+p(t)x'+x=0, \tag {4} \] \(x(t)\to 0\) as \(t\to \infty \).