5. Let y(x) be the solution to the differential equation

(x2+1)1/2dy - (x/y)dx = 0 satisfying y(31/2) = 3. Then [y(81/2)]2 =

A. 6

B. 8

C. 10

D. 11

E. 13

 

Solution: The answer is D

To solve the following differential equation,

Separate the variables and their corresponding differentials as follows,

Integrating the right side yields,

Integrate the left side by,

Equating both results yields,

Therefore,