Chapter 14, Problem 1PE

To determine

To discuss: The separable differential equation.

Answer to Problem 1PE

The separable differential equation is explained below.

Explanation of Solution

A separable differential equation is one that can be broken into a set of separate equations of lower dimensionality by using the method of separation of variables.

Or in the other wordsa separable differential equation is one that can be written in the form of:

  $\frac{dy}{dx}=\frac{g\left(x\right)}{f\left(y\right)}$

As shown, the above written equation can be solved by separating the variables and integrating each side as follows:

  ${\displaystyle \int f\left(y\right)}dy={\displaystyle \int g\left(x\right)}dx$