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## Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor. y(6x y 6) dx (6

Question

Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor. y(6x y 6) dx (6x 2y) dy

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Mathematics
3 years
2021-08-06T14:58:36+00:00
2021-08-06T14:58:36+00:00 1 Answers
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## Answers ( )

Answer:which implies that C is the integrating factor

Step-by-step explanation:The correct format for the equation given is:

By the application of the general differential equation:

⇒ Mdx + Ndy = 0

where:

M = 6xy+y²+6y

and

N = 6x +2y

∴

f(x) = 1

Now, the integrating factor can be computed as:

the integrating factor =

From the given equation:

Let us multiply the above given equation by the integrating factor:

i.e.

By rearrangement:

Let assume that:

and:

Then:

By integration:

which implies that C is the integrating factor