Question

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.

What does it mean for a differential equation to be separable?

Short answer

A differential equation is separable if the variables can be separated. The equation can be written in the form$y\text{'}=f\left(x\right)g\left(y\right)$.

Step-by-step solution

Step 1. Given Information.

The objective is to explain what does it mean for a differential equation to be separable.

Step 2. A differential equation is separable.

A differential equation is separable if the variables can be separated. The equation can be written in the form $y\text{'}=f\left(x\right)g\left(y\right)$.

A separable equation is as follows,

$F\left(y\right)dy=G\left(x\right)dx$.

It is a method in which we separate the variables and then integrate.