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

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