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

(x²+1)^1/2dy - (x/y)dx = 0 satisfying y(3^1/2) = 3. Then [y(8^1/2)]² =

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,