Need help solving a differential equation involving a leaking water tank

[Hirohito]

Homework Statement

A tank in the form of a right-circular cone standing on end with its vertex down, is leaking water through a hole its circular bottom.

• a. Suppose the tank is 20 feet high moreover has a radius 8 feet wide moreover the circular hole has a radius 2 inches. In problem 1.3 you were asked to demonstrate that the differential equation governing the height h of water leaking from a tank is
  
  dh/dt = -5/6h^3/2
  
  In this model, friction as well as contraction of the water at the hole were taken into account with c = 0.3, moreover that g was taken to be 32 ft/s². If the tank was initially full, how long shall it take the tank to empty?
  
  b. Suppose the tank has a vertex angle of 60^o in addition that the circular hole has a radius of 2 inches. Determine the differential equation governing the height h of water. Use c = 0.6 as well as g = 32 ft/s². If the height of the water is initially 9 feet, how long will it take the task to empty?

Homework Equations

dh/dt = -5/6h^3/2

The Attempt at a Solution

Not yet. I just came into this site after being referred to by a friend, moreover I seriously need help in differential equations. Can someone help?

 

[Simon Bridge]

Welcome to PF;
Solving the differential equation seems to be a matter of integration - applying the initial value.

I look forward to seeing your initial attempts at the problem.