5. Let y(x) be the solution to the differential equation
(x^{2}+1)^{1/2}dy - (x/y)dx = 0 satisfying y(3^{1/2}) = 3. Then [y(8^{1/2})]^{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,