# Homework Help: App of differentiation

1. Aug 15, 2010

### elitewarr

1. The problem statement, all variables and given/known data
dV/dT = 0.15(300-V)
V is the volume of water in a container at time T. The rate of water flowing into the container is constant at 45 units^3/s. The rate of water leaking is proportional to the volume of water currently in the container. Find the volume of water in the container when T = 20s. Initial volume of water = 0 units^3.

2. Relevant equations

3. The attempt at a solution
I tried integrating the equation but could not get any further. V is a function of time which means that I have no idea in doing this. Could anyone help me? Thanks.

2. Aug 15, 2010

### Pengwuino

First of all, what is the proportionality of the water leaking? By your equation, I'm assuming your vessel is losing water with a proportionality constant of 0.15/s?

This is a simple first order differential equation of the form $$y'[t] + ay[t] = b$$ where differentiation is with respect to time, t. Do you know how to use integrating factors?

3. Aug 15, 2010

### elitewarr

Ok. Thanks a lot. I have somewhat an idea of how to solve it.