(1+xy)xdy+(1-yx)ydx=0

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Here is a video of Non Exact Equation, we have used inspection method to solve the problem. Please watch the video with patience.
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Note:
Equations Reducible to Exact:
Sometimes, the differential equation Mdx+Ndy=0 is not exact. Suppose that, there exists a function F(x,y) such that
F(x,y)[Mdx+Ndy]=0 is exact, then F(x,y) is called an "Integrating factor" of the given differential equation Mdx+Ndy=0.
Inspection Method:
An integrating factor (I.F) of given equation
Mdx+Ndy=0 can be found by inspection as explained below. By rearranging the terms of the given equation or (and by dividing with a suitable function of x and y, the equation thus obtained will contain several parts integrable easily.
In this connection the following exact differentials will be found useful:
1. d(xy) = xdy+ydx
2. d[x/y] = [ydx-xdy]/y^2
3. d(y/x) = [xdy-ydx]/x^2
4. d[log(xy)] = [xdy-ydx]/xy
5. d(y^2/x) = [2xydy-y^2dx]/x^2
6. d(x^2/y) = [2xydx-y^2dy]/y^2
7. d(y^2/x^2) = [2(x^2)ydy-2x(y^2)dx]/x^4
8. d(x^2/y^2) = [2(y^2)xdx-2y(x^2)dy]/y^4
9. d[log(x/y)] = (ydx-xdy)/xy
10. d[arcTan(x/y)] = (ydx-xdy)/(x^2 + y^2)
11. d[arcTan(y/x)] = (xdy-ydx)/(x^2 + y^2)
12. d(e^x/y) = [y(e^x)dx-(e^x)dy]/y^2
13. d(e^y/x) = [x(e^y)dy-(e^y)dx]/x^2
14. d[log(x/y)] = (ydx-xdy)/xy
15. d[log(y/x)] = (xdy-ydx)/xy
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A differential equation can have more than one integrating factor.
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