 Hello friends, and how are you all doing today? My name is Priyanka. The question says sort the following differential equation Now I have the differential equation which is given to us is dy by dx minus y is equal to x into e raised to the power x Let us quickly proceed with the solution. We are given the differential equation is dy by dx minus y is equal to x e raised to the power x Now it is a first order differential equation where p is equal to minus 1 and Q is equal to x e raised to the power x, right? So the integrating factor here will be e raised to the power p dx that is minus 1 dx which is equal to e raised to the power minus x Now multiplying integrating factor to the required to find out the required solution is y into integrating factor equal to Q into integrating factor into sorry integral of Q into integrating factor into dx plus C. So here we have y into e raised to the power minus x equal to x square upon 2 plus C, which is y is equal to x square upon 2 divided by e raised to the power minus x plus C which can be written as y is equal to x square e raised to the power x upon 2 Plus here also we had e raised to the power minus x as its divisor Sorry as the number which is dividing it. So we have e raised to the power x with C So the answer to the question is Y is equal to taking e raised to the power x common x square upon 2 plus C So this is the required answer to the question Right, so hope you understood it well and enjoyed it too. Have a nice day ahead