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## Main Question or Discussion Point

I've tried almost everything but i still get stuck when finding the integral of :

(2x^2y-e^(-x^2))dx+(x+1)dy =0

To attempt to solve it i did the following:----> since the DE is not exact :

1) [M(x,y)/dy - N(x,y)/dx]/N(x,y) = [2x^2-1/x+1]

2) ∫[2x^2-1/x+1] =

3) Integrating Factor: e^(x^2 - 2x +ln|x|) to make it smaller I'm gonna call

{e^(x^2 - 2x +ln|x|)} = P

4) P*[(2x^2-e^-(x^2))dx + (x+1)dy] =0

After simplifying I get: [(2x^2)ye^(x^2)-1]dx = [e^(x^2)](x+1)dy

After that I don't know what to do.

(2x^2y-e^(-x^2))dx+(x+1)dy =0

To attempt to solve it i did the following:----> since the DE is not exact :

1) [M(x,y)/dy - N(x,y)/dx]/N(x,y) = [2x^2-1/x+1]

2) ∫[2x^2-1/x+1] =

3) Integrating Factor: e^(x^2 - 2x +ln|x|) to make it smaller I'm gonna call

{e^(x^2 - 2x +ln|x|)} = P

4) P*[(2x^2-e^-(x^2))dx + (x+1)dy] =0

After simplifying I get: [(2x^2)ye^(x^2)-1]dx = [e^(x^2)](x+1)dy

After that I don't know what to do.