Answer:
Yes , it is separable
Step-by-step explanation:
We are given that DE
[tex]\frac{dy}{dx}-2y=16+3xy+24x[/tex]
We have to find the the given DE is separable or not.
[tex]\frac{dy}{dx}-2y=16x+3xy+24x[/tex]
[tex]\frac{dy}{dx}=16+3xy+24x+2y[/tex]
[tex]\frac{dy}{dx}=16+24x+3xy+2y=8(2+3x)+y(3x+2)[/tex]
[tex]\frac{dy}{dx}=(2+3x)(8+y)[/tex]
[tex]\frac{dy}{8+y}=(2+3x)dx[/tex]
When the DE is separable then it can be written as
[tex]p(y)dy=q(x)dx[/tex]
Given DE is in Separable form.Therefore, it is separable.
