Differential equation Problem with separating variables

Question

I'm having difficulties, generally, with solving problems with differential equations. I hope to see a pattern and find solutions eventually myself by having detailed solutions to for example the following question:

1. Depth h of water in a tank at time t minutes is decreasing at a rate which is proportional to √h. The initial depth of water is 200cm and the depth after 5 minutes is 128cm. a) find h as a function of t. b) find how long it will take for the tank to empty.
A) I started with setting dh/dt=-k√h, is that right? As it is a decreased function. The thing is, I'm stuck after integration. The integrate would be, I believe: 2h^1/2=-kt + c. 

 Then h=(-kt+c)²/2

Resulting in c=√800

However, the solution says c=10. If I go back, that could only mean they got

h=2(-kt+c)²

But then they must've integrated h wrong. Did I get the differential equation in the beginning wrong? I'm really confused and would be very grateful for some help. 

Answer 1

You wrote... The integrate (integral, or antiderivative) would be, I believe: 2h^1/2=-kt + c.    correct!

 

But then you said:  Then h=(-kt+c)2/2     h should be the square of  [(-kt+C) / 2]