Question

Determine whether or not the given differential equation is separable, that is, whether it can be expressed in the form p(y) dy = q(x) dx. dy/dx − 2y = 16 + 3xy + 24x

Answer 1

Answer:

Yes , it is separable

Step-by-step explanation:

We are given that DE

$\frac{dy}{dx}-2y=16+3xy+24x$

We have to find the the given DE is separable or not.

$\frac{dy}{dx}-2y=16x+3xy+24x$

$\frac{dy}{dx}=16+3xy+24x+2y$

$\frac{dy}{dx}=16+24x+3xy+2y=8(2+3x)+y(3x+2)$

$\frac{dy}{dx}=(2+3x)(8+y)$

$\frac{dy}{8+y}=(2+3x)dx$

When the DE is separable then it can be written as

$p(y)dy=q(x)dx$

Given DE is in Separable form.Therefore, it is separable.