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#### find_the_fun

##### Active member

- Feb 1, 2012

- 166

So \(\displaystyle M(x, y) = 5x+4y\) and \(\displaystyle N(x, y) = 4x-8y^3\)

Check \(\displaystyle \frac{\partial M}{\partial y} = 4\) and \(\displaystyle \frac{ \partial N}{\partial x} = 4 \) check passed.

\(\displaystyle f(x, y) = \int M \partial x + g(y) = \int 5x+4y \partial x + g(y) = \frac{5x^2}{2} + 4yx + g(y) \)

\(\displaystyle \frac{\partial f(x, y)}{\partial y} = g'(y) = 4x-8y^3\)

Therefore \(\displaystyle g(y) = 4xy-2y^4\)

So \(\displaystyle f(x, y)=\frac{5x^2}{2}+4yx+4yx-2y^4\)

The back of book has only one 4yx so what did I do wrong? Also the back of the book has the equation \(\displaystyle =C\) and I don't understand why?