integrating factor!

**lawochekel** · September 4th 2012, 06:17 AM

$[x^2\exp^\frac{y}{x}-y^2]dx + xydy = 0$

pls refer to the above equation, i need help on how to solve for the integrating factor, thanks!

**pickslides** · September 4th 2012, 02:50 PM

To find an intgrating factor arrange the equation into the form

$\displaystyle \frac{dy}{dx}+ p(x)\times y = q(x)$

Once you have done this the integrating factor is simply $\displaystyle e^{\int p(x) dx}$

**Prove It** · September 4th 2012, 06:37 PM

Originally Posted by pickslides

To find an intgrating factor arrange the equation into the form

$\displaystyle \frac{dy}{dx}+ p(x)\times y = q(x)$

Once you have done this the integrating factor is simply $\displaystyle e^{\int p(x) dx}$

Not in this case Pickslides. What the OP has is an equation which he/she hopes can be multiplied by a function to be turned into an EXACT differential equation. This function we are trying to find is also called an integrating factor.

**lawochekel** · September 5th 2012, 02:33 AM

thanks alot "prove it", the material proved very helpful.

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