Chapter 4.7, Problem 27E

To determine

$\left(a\right)$

To verify:

Two solutions of the equation. And show that $y_1\left(t_0\right)y_2{}^{\prime }\left(t_0\right)-y_1{}^{\prime }\left(t_0\right)y_2\left(t_0\right)\ne 0$ for $t_0=1$.

To determine

$\left(b\right)$

To prove:

The linearly independency of two functions on $\left(-\infty ,\infty \right)$.

To determine

$\left(c\right)$

To verify:

The function as a solution of the equation on $\left(-\infty ,\infty \right)$.

To determine

$\left(d\right)$

To prove:

There does not exist constants with the given condition.

To determine

$\left(e\right)$

To find:

A counterexample.