(a) Show that every member of the family of functions y = (6 ln(x) + C)/x , x > 0, is a solution of the differential equation x2y' + xy = 6. (Simplify as much as possible.)

Therefore , every element of the function is a solution of the DE  .

Step-by-step explanation:

Given differential equation is

[ divided by x²]

Here and

The integrating factor is =  

                                        = x

Multiplying the integrating factor both sides of the ODE

   [ ]

Integrating both sides

  [ c is an arbitrary constant]

        for x>0

Therefore , every element of the function is a solution of the DE  .