 Hi and welcome to the session. Let's work out the following question. The question says solve the following differential equation That is dy by dx minus y by x is equal to 2x squared So let us start with the solution to this question. Now we are given dy by dx minus y by x is equal to 2x squared. It is a linear differential equation of the form dy by dx plus p by is equal to q where p is equal to minus 1 by x and q is equal to 2x squared Integrating factor will be e raised to power integral p dx that is e raised to power integral minus 1 upon x dx That is equal to e raised to power minus log x that is equal to e raised to power log x inverse That is equal to x inverse and that is equal to 1 upon x Now for such a linear differential equation The solution is given by y into integrating factor that is 1 upon x is equal to integral of q that is 2x squared into integrating factor that is 1 by x dx Plus a constant say c This implies that y by x is equal to this becomes 2x and 2x on integration gives x squared plus c Multiplying both the sides by x we get y is equal to x cubed plus c into x So this is our answer to this question. I hope that you understood this solution and enjoyed the session. Have a good day