Answer: Determine whether each of the equations in 1 through 8 is exact. If it is exact

Step 1 of 2

Given differential equation is \((2 x+3)+(2 y-2) y^{\prime}=0\)

Rewrite the differential equation as,

\((2 x+3) d x+(2 y-2) d y=0\) 

Now, a differential equation of the form \(M d x+N d y=0\) is called exact D.E if

\(\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}\) 

Comparing the differential equations we have,

\(M=2 x+3, N=2 y-2\) 

Differentiating M and N with respect to x and y,

\(\frac{\partial M}{\partial y}=0, \frac{\partial N}{\partial x}=0\) 

So, \(\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}\)