Question: Consider the following differential equation. ( x y 7 + y 2 sin( x )) dx = (7 xy 6 + 2 y cos( x

Consider the following differential equation.

(xy7+y2sin(x))dx= (7xy6+ 2ycos(x))dy

LetM=y7y2sin(x)x

andN=7xy6+ 2ycos(x).

Find the following partial derivatives.

My

=Nx

=

Is the given differential equation exact?

Yes

No

Letf

x

=y7y2sin(x)x.

Integrate this partial derivative with respect tox, lettingh(y)

be an unknown function iny.

f(x,y) =+h(y)

Find the derivative ofh(y).

h(y) =

Find the general solution of the given differential equation. (If it is not exact, enter NOT.)

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