Question

show that y = x - x^(-1) is a solution to the differential equation xy'+x=2x

Answer 1

find y' , then substitute it into your differential equation

Answer 2

All you need here is to substitute the solution into the differential equation and see if the equation holds. We have \(y=x-x^{-1} \implies y'=1+x^{-2}\). Substituting this gives:
\(x(1+x^{-2})+x=2x+x^{-1}\). This is different from the right hand side, so it's not a solution. Are you sure about the solution you gave?!

Answer 3

no it is right thank you for your help, it is a solution!