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bezimeni [28]
2 years ago
12

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
Mathematics
1 answer:
Flura [38]2 years ago
7 0

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.

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