(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  .

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

p = 6s

step-by-step explanation: