00:01
Consider 18 x square y plus 2 x y plus 6 y cube dx plus x square plus y square dy is equals to 0.
00:18
This is not the this is the form of m dx plus n dy is equals to 0.
00:27
Here m is equals to 18 x square y plus 2 x y plus 6 y cube and n is equals to x square plus y square.
00:39
So here delta m divided by delta y is equals to delta divided by delta y or we can say it is d and here 18 x square y plus 2 x y plus 6 y cube.
00:59
So it is equals to 18 x square plus 2 x plus 18 y square.
01:06
Now delta n divided by delta x is equals to delta divided by delta x that means x square plus y square is equals to 2 x.
01:20
Clearly delta m divided by delta y is not equal to delta n divided by delta y.
01:29
Therefore the given differential equation is not exact.
01:32
We have to make it exact by multiplying both m and n with appropriate integrating factor.
01:40
Check m1 minus n1 divide by n is not a sorry is a factor of x minus q in the bracket x.
01:57
So it is equals to 18 x square plus 2 x plus 18 y square minus 2 x divide by x square plus y square...