Solve the following equation.
( 3x2y4 + 2xy ) dx + ( 2x3y3 - x2 ) dy = 0
The Attempt at a Solution
M = ( 3xy4 + 2xy )
N = ( 2x3y3 - x2 )
∂M/∂y = 12x2y3 + 2x
∂N/∂x = 6x2y3 - 2x
Then this equation looks like that the integrating factor is (xM-yN).
IF = x3y4 + 3x2y
then the new equation would be:
(3xy^3+2)/(x^2y^3+3x)dx + (2xy^3-1)/(xy^4+3y)dy = 0
but then if we find that this new equation is exact or not, it proves that this is not exact.
If so what should I do?
The given answer is:
x3y2 + x2/y = c