00:01
In the question we have to verify that the new equation is exact and the given equation is given equation is y square plus 2xy multiply by dy plus x square plus 2xy multiply by dx is equal to y square dx plus x square dy.
00:25
So we can further write it as y square plus 2xy minus x square dy plus x square plus 2xy minus y square dx is equal to 0.
00:43
Let us take this as equation 1.
00:45
So we know that the differential equation that is m dx plus n dy is equal to 0 is exact if del m by del y will be equal to del n by del x.
01:07
So here we have m x comma y is equal to x square plus 2xy minus y square and n x comma y is equal to y square plus 2xy minus x square.
01:26
So we will find dm by dy that means we will differentiate m with respect to y so we will get 2x minus 2y and we will find del m by del x that is del n by del x that is we will differentiate n with respect to x so we will get 2y minus 2x.
01:49
Therefore we clearly see that del m by del y is not equal to del n by del x.
01:58
Hence we can say that equation 1 is not exact.
02:06
Now we will multiply equation 1 by integrating factor that is u x comma y is equal to x plus y to the power minus 2.
02:19
So we will get x square plus 2xy minus y square upon x plus y whole square dx plus y square plus 2xy minus x square upon x plus y whole square dy is equal to 0.
02:43
Let us take this as equation 2...