Section 4.4.1: 1, 2, 3, 4, 5, 6, 7, 8

Also:

1. Suppose $p$ and $q$ are continuous functions on an open interval $J$, and that $y_1$ and $y_2$ are both solutions of $y'' + p(t)y' + q(t)y = 0$ on $J$. Moreover, suppose that for some $t_0$ in $J$, $y_1(t_0) = 0$ and $y_2(t_0) = 0$. Show that $y_1$ and $y_2$ are not a fundamental set of solutions for the equation on $J$.
2. Suppose $p$ and $q$ are continuous functions on an open interval $J$, and that $y_1$ and $y_2$ are both solutions of $y'' + p(t)y' + q(t)y = 0$ on $J$. Moreover, suppose that $y_1$ and $y_2$ both achieve a maximum value at some point $t_0$ in $J$. Show that $y_1$ and $y_2$ are not a fundamental set of solutions for the equation on $J$.