00:01
In this problem, we are asked to solve the differential equation x squared minus 4 times xy d x plus x ,dy equals to 0.
00:14
So here we have m equals to x squared minus 4 xy and we have n equals to x.
00:26
So partially differentiating m with respect to y, we get negative 4x and partially differentiating n with respect to x, we get 1.
00:37
Clearly, mi does not equal to nx.
00:41
So we require the integrating factor.
00:44
For that, we first find out mi minus nx the whole divided by n.
00:49
So we get negative 4x minus 1, the whole divided by x, which simplifies.
00:57
To negative of 4 plus 1 over x.
01:08
So now let us integrate this integral of my minus nx the whole divided by n dx equals to integral of negative of 4 plus 1 over x d x.
01:21
So integrating this we have negative 4x 4x 4x to simplify this, we can write this as negative 4x plus natural log of 1 over x.
01:42
So for the integrating factor, we have e raised to the power of integral, my minus nx over n dx.
01:54
So in this case we have e raised to the power negative 4x plus natural log of 1 over x.
02:00
This can be split and written as e raised to the power negative 4x plus natural log of 1 over x.
02:04
X times e raised to the power natural log of 1 over x...