Question

Determine whether the following equation is exact. If it is,then solve it.

Answer 1

\((2x+y)dx+(x-2y)dy=0\)

Answer 2

Is it valid,if we do like this?
\((2x+y)dx-(2y-x)dy=0\)
Because if we didnt change the sign,it will not become an exact equation.

Answer 3

\(\frac{dM}{dx}=2\) , \(\frac{dN}{dy}=-2\)
\(\frac{dM}{dx}\neq\frac{dN}{dy}\)