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.