(x^3y^3+x^2y^2+xy+1)ydx+(x^3y^3-x^2y^2-xy+1)xdy=0 #NonExact L583 @MathsPulseChinnaiahKalpana

#reducibletoexact #nonexactequation

Hello, People!

Here is a video of Non-Exact equation problem, which is reducible to exact using integrating factor(I.F.) 1/Mx-Ny.

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Chinnaiah Kalpana🍁

Note:

* Method:

If the equation Mdx+Ndy=0 is of the form
yf(xy)dx+xf(xy)dy=0 and Mx-Ny≠0
then 1/Mx-Ny is an integrating factor of Mdx+Ndy=0.

* If Mx-Ny=9, then M/N=y/x. Then the equation reduces to ydx+xdy=0.

* Working rule to solve Mdx+Ndy=0:

1. General equation is Mdx+Ndy=0 -----(i)
observe (partial derivative of M w.r.t y)≠
(partial derivative of N w.r.t x),
then (i) is not exact.

2. Observe (i) is of the form
yf(xy)dx+xg(xy)dy=0.

3. Find Mx-Ny and observe it ≠0.
Then 1/Mx-Ny is an I.F. of (i).

4. Multiply (i) with I.F. to transform it into an exact equation of (i) M1dx+N1dy=0 ----(ii)

5. Solve (ii) to get the general solution of (i).

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