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I thought I got this problem wrong, but I think I have it right now. It turned out that when I was taking the derivative of e^xy

(y

First, I test to make sure it's exact. When I differentiate the first with respect to y, and the second with respect to x, I get 2xy

When I integrate (y

The derivative of e^xy

So my final function is f(x,y) = e^xy

^{2}with respect to y, I forgot that you're supposed to multiply by 2xy (the derivative of xy^{2}), not just x.## Homework Statement

(y

^{2}* e^xy^{2}+ 4x^{3}dx + (2xy * e^xy^{2}- 3y^{2}dy = 0## Homework Equations

## The Attempt at a Solution

First, I test to make sure it's exact. When I differentiate the first with respect to y, and the second with respect to x, I get 2xy

^{3}* e^xy^{2}+ 2y*e^xy^{2}for both, so it is indeed exact.When I integrate (y

^{2}* e^xy^{2}+ 4x^{3}dx, I get e^xy^{2}+ x^4 + f(y)The derivative of e^xy

^{2}+ x^4 + f(y) with respect to y is 2xy*e^xy^{2}+ f'(y), and f'(y) is (2xy * e^xy^{2}- 3y^{2}dy), so I integrate 3y^{2}with respect to y, and get y^{3}So my final function is f(x,y) = e^xy

^{2}+ x^{4}+ y^{3}
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