Understanding Water Flow in a Leaky Container Using Differentiation

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SUMMARY

The discussion focuses on solving a first-order differential equation representing water flow in a leaky container, defined by the equation dV/dT = 0.15(300-V). The volume of water, V, is influenced by a constant inflow rate of 45 units³/s and a leakage rate proportional to the current volume. The initial volume is 0 units³, and the goal is to determine the volume at T = 20s. Participants clarify the proportionality constant for the leakage and suggest using integrating factors for solving the equation.

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Homework Statement


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.


Homework Equations





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

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