Chapter 2.5, Problem 5E

Interpretation Introduction

Interpretation:

It is to be proved that ${\dot{\text{x}}\text{ = |x|}}^{\frac{\text{p}}{\text{q}}}\text{, x(0)=0}$ has an infinite number of solutions if $\text{p < q}$ and has a unique solution if $\text{ p > q}$.

Concept Introduction:

The existence and uniqueness theorem states that ‘$\text{f(x)}$, and $\text{f'(x)}$ are continuous on an open interval R of the x-axis, and suppose that ${\text{ x}}_0$ is a point in R. Then the initial value problem has a solution $\text{x(t)}$ on some time interval $\text{(-t,t)}$ about $\text{t = 0}$, and the solution is unique’.