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y(1+xy)dx+x(1-xy)dy=0 #NonExact L575 @MathsPulseChinnaiahKalpana
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#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.
My hearty thanks to all the subscribers, supporters, viewers and well-wishers❤
With Love,
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).
For more such videos👇
Stay tuned to 'Maths Pulse'.
Get rid of 'Maths Phobia'.
Have a happy learning!
#chinnaiahkalpana #mathspulse #engineeringmathematics #bscmathsproblems #nonexactproblems #reducibletoexactproblems
Hello, People!
Here is a video of Non-Exact equation problem, which is reducible to exact using integrating factor(I.F.) 1/Mx-Ny.
My hearty thanks to all the subscribers, supporters, viewers and well-wishers❤
With Love,
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).
For more such videos👇
Stay tuned to 'Maths Pulse'.
Get rid of 'Maths Phobia'.
Have a happy learning!
#chinnaiahkalpana #mathspulse #engineeringmathematics #bscmathsproblems #nonexactproblems #reducibletoexactproblems
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