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I have the following partial derivatives

∂f/∂x = cos(x)sin(x)-xy^{2}

∂f/∂y = y - yx^{2}

I need to find the original function, f(x,y).

I know that df = (∂f/∂x)dx + (∂f/∂y)dy

and hence

f(x,y) = ∫∂f/∂x dx + g(y) = -1/2(x^{2}y^{2}+cos^{2}(x)) + g(y)

Then to find g(y) I took the partial derivative of f(x,y) that I just found wrt y and equate to the original given ∂f/∂y

i.e -x^{2}y +g'(y) = y-x^{2}

which is a first order differential equation of the form

dg/dy = - (y+x^{2})/(x^{2}y)

and now I am not sure how to proceed and solve this DE

Mitch

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# Finding a function given its partial derivatives, stuck on finding g'(x)

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