Chapter 7, Problem 4RQ

To determine

whether the statement is true or false

Answer to Problem 4RQ

The statement is true

Explanation of Solution

Given information : The question is

The equation $y\text{'}=3y-2x+6xy-1$ is separable

For this equation to be separable it would have to be able to write $3y-2x+6xy-1$ from the equation $y\text{'}=3y-2x+6xy-1$ in the form of $f\left(x\right)g\left(y\right)$ where $f\left(x\right)$ is the function of $x$ only and in $g\left(y\right)$ is the function of $y$ only

  $\begin{array}{l}y\text{'}=3y-2x+6xy-1\\ y\text{'}=6xy+3y-2x-x\\ \Rightarrow \left(3y-1\right)\left(2x+1\right)\end{array}$

Therefore, the equation $y\text{'}=3y-2x+6xy-1$ is written in the form of $f\left(x\right)g\left(y\right)$ where $f\left(x\right)$ is $\left(2x+1\right)$ and $g\left(y\right)$ is $\left(3y-1\right)$