Question

How to work on this,
2(2x^2 + y^2)dx - xydy =0

Answer 1

http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

Answer 2

this is a toughy

Answer 3

\(M(x,y) = 2(2x^2 + y^2)\)
\(N(x,y) = -xy\)

\(M_{y}(x,y) = 4y\)
\(N_{x}(x,y) = -y\)

That's not quite exact, but it is a clue.

\(\dfrac{M_{y} - N_{x}}{N(x,y)} = -5/x = Q(x)\)

\(\int Q(x)\;dx = -5\cdot \ln|x| + C\)

\(e^{-5\cdot \ln|x| + C} = \dfrac{A}{x^{5}} = u(x)\)

Now, see if it's exact.
\(M(x,y)\cdot u(x) = \)
\(N(x,y)\cdot u(x) = \)