Chapter 5.4, Problem 39P

(a)

To determine

The condition on $\alpha$ such that all solution of the Euler equation approach zero as $x\to 0$.

(b)

To determine

The condition on $\alpha \text{ and }\beta$ such that all solution of the Euler equation are bounded as $x\to 0$.

(c)

To determine

The condition on $\alpha \text{ and }\beta$ such that all solution of the Euler equation approaches 0 as $x\to \infty$.

(d)

To determine

The condition on $\alpha \text{ and }\beta$ such that all solution of the Euler equation are bounded as $x\to \infty$.

(c)

To determine

The condition on $\alpha \text{ and }\beta$ such that all solution of the Euler equation approaches 0 as $x\to 0\text{ and }x\to \infty$.