- #1

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## Homework Statement

Solve the following equation.

## Homework Equations

( 3x

^{2}y

^{4}+ 2xy ) dx + ( 2x

^{3}y

^{3}- x

^{2}) dy = 0

## The Attempt at a Solution

M = ( 3xy

^{4}+ 2xy )

N = ( 2x

^{3}y

^{3}- x

^{2})

∂M/∂y = 12x

^{2}y

^{3}+ 2x

∂N/∂x = 6x

^{2}y

^{3}- 2x

Then this equation looks like that the integrating factor is (xM-yN).

IF = x

^{3}y

^{4}+ 3x

^{2}y

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?

Please help...

Note:

The given answer is:

x

^{3}y

^{2}+ x

^{2}/y = c