Question

Show that the function is a solution of the differential equation.

Function                                      Differential Equation

y = 2 lnx + 3                                  xy" + y' = 0

Answer 1

Step 1:

The function is .

Apply derivative on each side with respect to .

Apply the constant rule of derivative : .

Apply the logarithm rule of derivative : .

Step 2:

Apply derivative on each side with respect to .

Apply the power rule of derivative : .

Rewrite the above equation,

Substitute in above equation.

The differential equation is

Solution :

The solution of the differential equation is