Show that if \(x_1(t)\) and \(x_2(t)\) are solutions of \(x''+p(t)x'+q(t)x=0\), then so is \(x(t)=c_1x_1 + c_2x_2\).
Find two constants \(\lambda_1\) and \(\lambda_2\) such that \(e^{\lambda_1t}\) and \(e^{\lambda_2t}\) are each solutions of \(x''+3x'+2x=0\). Then verify that \(c_1e^{\lambda_1t}+c_2e^{\lambda_2t}\) is also a solution.
Show that if \(x_1(t)\) and \(x_2(t)\) are solutions of \(x''+p(t)x'+q(t)x=0\), and there exists \(t_0\) such that \(W(x_1, x_2)(t_0)\neq0\), then \(W(x_1, x_2)(t)\neq0\) for all \(t\).
(3.1) 10, 12, 14, 16, 18