Chapter 2.3, Problem 1E

Interpretation Introduction

Interpretation:

The logistic equation $\dot{\text{N}}\text{ = rN}\left(\text{1 - }\frac{\text{N}}{\text{K}}\right)$ is to be solved analytically for an arbitrary initial condition ${\text{N}}_{\text{0}}$ using partial fractions and making the change of variable $\text{x = }\frac{\text{1}}{\text{N}}$.

Concept Introduction:

The given equation can be solved by separating the variables using partial fractions and integrating both sides.

The equation can also be solved by making the change of variable and integrating both the sides.

By substituting the initial condition, the constant of integration could be found.