00:01
In this question, we are given a differential equation 4x square plus 3y square dx minus 2xy dy equals 0 and we have to solve for y.
00:17
So, let us assume that m equals 4x square plus 3y square and n equals minus 2xy.
00:29
So, del m over del y will be equals to 6y and del n over del y will be equal to minus 2y.
00:44
So, this is del n over del x will be equals to minus 2y.
00:50
Here, we can clearly see that del m over del y is not equals to del n over del x.
00:59
So, we can say that 1 by n sorry 1 by n multiplied by del m over del y minus del n over del x equals 1 over minus 2xy 6y plus 2y that is equals to minus 8y over 2xy that is equals to minus 4 over x and this is equals to f of x.
01:40
Hence, we consider del f will be equals to e raise to power integration of f of x that is e integration minus 4 over x dx that turns out to be e raise to power minus 4 ln x or we can write this as e raise to power ln x raise to power minus 4.
02:10
Now, this can be written as 1 over x raise to power 4.
02:15
Now, we can let us say this is our first equation that is the given equation.
02:24
So, if we multiply equation 1 with 1 over x raise to power 4, we will get that 4x square plus 3y square over x raise to power 4 dx minus 2xy over x raise to power 4 dy will be equals to 0...