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,

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Since v does not appear on the right-hand-side of the equation, this is a simple integration.
h depends on v by a second equation the OP didn't write down.

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