Chapter 3 - Second Order Linear Equations - 3.2 Solutions of Linear Homogenous Equations; the Wronskian - Problems - Page 155: 10

$(0,\infty)$

$y''+cos(t)y'+3ln|t|y=0$ To use Theorem 3.2.1: $p(t)=cos(t)$ which is continuous on $(-\infty,\infty) $ $q(t)=3ln|t|$ which is continuous on $(0,\infty) $ $g(t)=0$ which is continuous on $(-\infty,\infty) $ Thus, $p(t),q(t),$ and $g(t)$ are all continuous on $(0,\infty) $ Since $t_0=2$, the solution exists on $(0,\infty) $