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#### alane1994

##### Active member

- Oct 16, 2012

- 126

Ok, so I have this differential equation.

\[(3x^2y+2xy+y^3)+(x^2+y^2)y\prime=0\]

First I needed to check to see if it is exact.

\(M=3x^2y+2xy+y^3\)

\(N=x^2+y^2\)

\(\dfrac{\partial M}{dy}(3x^2y+2xy+y^3)=3x^2+2x+3y^2\)

\(\dfrac{\partial N}{dx}(x^2+y^2)=2x+0\)

For the integrating factor, I believe it is in the form,

\[\dfrac{M_y(x,y)-N_x(x,y)}{N(x,y)}\mu\]

And so, I would have,

\(\dfrac{3x^2+2x+3y^2-2x}{x^2+y^2}\mu = \dfrac{3x^2+3y^2}{x^2+y^2}\mu=\dfrac{d\mu}{dx}\)

Now... I feel as though I am wrong in this. Could someone look and tell me if I am on the right track, and if I am off guide me back to the path of righteousness?

\[(3x^2y+2xy+y^3)+(x^2+y^2)y\prime=0\]

First I needed to check to see if it is exact.

\(M=3x^2y+2xy+y^3\)

\(N=x^2+y^2\)

\(\dfrac{\partial M}{dy}(3x^2y+2xy+y^3)=3x^2+2x+3y^2\)

\(\dfrac{\partial N}{dx}(x^2+y^2)=2x+0\)

For the integrating factor, I believe it is in the form,

\[\dfrac{M_y(x,y)-N_x(x,y)}{N(x,y)}\mu\]

And so, I would have,

\(\dfrac{3x^2+2x+3y^2-2x}{x^2+y^2}\mu = \dfrac{3x^2+3y^2}{x^2+y^2}\mu=\dfrac{d\mu}{dx}\)

Now... I feel as though I am wrong in this. Could someone look and tell me if I am on the right track, and if I am off guide me back to the path of righteousness?

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