00:01
So, we have given here the function that is y into e to the power 4xy plus x and into we have given here that is dx plus b into x e to the power 4xy into dy that is equal to we have given here 0.
00:35
Now we need to compare this equation into standard form and the standard equation we have here that is green's theorem standard equation that is mdx plus n dy is equal to 0.
00:54
Now for exact for exact differential equation we need to satisfy this condition here by the equation that is dm upon del m upon del y plus is equal to del n upon del x.
01:13
So, this equation must be satisfied from this given equation.
01:19
So, first we need to write here our m value that is equal to we have here y into e to the power 4xy plus x and we have our n value that is equal to bx e to the power 4xy.
01:42
Now we need to differentiate this m coefficient with respect to y that is equal to then 4xy e to the power 4xy plus e to the power 4xy that is a differential equation.
02:14
So, from here we have to write this equation as dm upon del m upon del y is equal to take e to the power 4xy common then we will get from here that is 4xy plus 1 and now we need to find here the value of del n upon del x.
02:40
So, that is equal to then we have here that is taking b outside we will get 4xy e to the power 4xy plus e to the power 4xy and this coefficient is multiplied with both term.
03:07
So, we have to write this equation as b into take e to the power 4xy common then we will get 4xy plus 1...