(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(y-x^3) + (x+y^3)y' = 0

equation is convenienty already in the required form, that is M_(x,y) + N_x(x,y)dy/dx = 0

so..

M_y = 1 = N_x therefore equation is exact. Therefore I now solve...

I am solving for a function, f(x,y) whose partial derivative with respect to y = M

and whose partial with respect to x = N.

Is this correct?

assuming correct so far, my next step is to integrate the M term, with respect to x

integ M_x (y-x^3) = -(1/4)x^4 + h(y)

i have a questions about this step though:

if y's are treated as constants when integrating, wouldn't the y in this equation become yx?

so that integ_x (y-x^3) = yx -(1/4)x^4 + h(y)

??

assuming yx is not in the integrated result, my next step is to take derivative of the just integrated M term, now with respect to y:

derivative of just-integ M_y [-(1/4)x^4 + h(y) ] = h'(y)

so i know that h'(y) = N term which is:

h'(y) = (x+y^3)

But i think im going to stop here because it looks sort of weird and i want to make sure its right so far.

thanks for any help

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Please check my work (exact equation, then i solved)

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