 Good morning friends, I am Purva and today I will help you with the following question. The integrating factor of the differential equation x into dy by dx minus y is equal to 2x square is a e raised to the power minus x, b e raised to the power minus y, c 1 upon x dx. Now, the integrating factor of the linear differential equation dy by dx plus px is equal to q is given by e raised to the power integral p dx. So, this is the key idea behind our question. Let us now begin with the solution. Now, the given differential equation is x into dy by dx minus y is equal to 2x square. Now, dividing both the sides by x we get or dy by dx minus 1 upon x into y is equal to 2x. Now, by comparing this equation with the equation in the key idea that is dy by dx plus px is equal to q, we can clearly see that p is equal to minus 1 upon x. So, here we have p is equal to minus 1 upon x. Therefore, the integrating factor of this equation is given by e raised to the power integral p dx and which is equal to e raised to the power integral minus 1 upon x dx. And this is equal to e raised to the power now integral of minus 1 upon x with respect to x is minus log x. So, we get e raised to the power minus log x and this is equal to e raised to the power log 1 upon x and this is equal to 1 upon x because e raised to the power log 1 upon x is equal to 1 upon x. So, we get the integrating factor as 1 upon x and this is same as option c. Hence, the correct option is c. This is our answer. Hope you have understood the solution. Bye and take care.