Problem with Integration of a function

So, I was working on project to calculate the sinking time of a ship, I draw it on SolidWorks, and calculated its Volume, and intial submerged height. Now Im stuck at this part

Introduce a hole at the lowest point in the hull and calculate the height of boatside above sea-water at any instant of time simultaneously employing numerical integration and solution of O.D.E.

I would apprechiate anyhelp going forward,

[Star Strider]

Since v does not appear on the right-hand-side of the equation, this is a simple integration.

[Torsten]

h depends on v by a second equation the OP didn't write down.