 Hi and how are you all today? The question says solve the differential equation. Here we are given x dy by dx minus y minus 2x cube is equal to 0. Let us quickly proceed with our solution, rewriting the given differential equation. Now here we can write this. Now as dy by dx is equal to y plus 2x cube whole upon x. Which can further be written as dy by dx is equal to y by x plus 2x square. So we have dy by dx minus y by x equal to 2x square. So now we can see that this differential equation is of the type dy by dx plus py is equal to cube. Therefore integrating factor will be equal to e raised to the power integral p dx. So y into integral factor will be equal to integral cube into integrating factor dx. Now here we can see that our p is equal to this is 1. So minus 1 by x this is p and this is our cube. So let us find out the integrating factor. Integrating term is equal to e raised to the power integral p dx. Here p is minus 1 upon x dx. So it is equal to e raised to the power minus log x which is further equal to 1 by x. So here our integrating factor is 1 upon x. Therefore solution is y into integrating factor equal to integral cube into integrating factor dx. This implies y upon x is equal to 2x square upon 2 plus c which is further equal to y is equal to multiplying x with all the terms in the right hand side we have x cube plus cx. Now here c was our constant of integration. So this is our required answer to the given question. Hope you understood it well and enjoyed it too. Have a nice day.