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May 29th, 2012, 03:53 PM   #1
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help me, differential equation

When mixing a certain alcoholic beverage, a barperson starts with a 10 litre solution
of 20% alcohol. Into this solution the barperson mixes a 40% alcohol
mixture at the rate of 1 litre/minute and pours into glasses at the rate of
2 litres/minute.
(a) Find a formula for the volume V (t) of the mixture at time t minutes.
(b) Find a differential equation that tells the rate of change of the amount
of alcohol A(t) at time t minutes.
(c) Solve the differential equation and use the initial condition to find a
formula for A(t)

dont know hard qs, can u help me
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May 29th, 2012, 09:59 PM   #2
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Re: help me, differential equation

There's no need to bump a topic after a few hours. It will be seen and someone will come along and help. If after a few days no one does, then its okay to bump it, preferably with some work or thoughts on how to proceed.
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May 29th, 2012, 10:02 PM   #3
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Re: help me, differential equation

sorry but i am doing my practice now and want to finish
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May 29th, 2012, 10:04 PM   #4
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Re: help me, differential equation

Post your thoughts about what you should do, and when I log on tomorrow, I promise I will help.
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May 29th, 2012, 10:42 PM   #5
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Re: help me, differential equation

ok i wait for u
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May 30th, 2012, 04:43 AM   #6
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Re: help me, differential equation

This is as good as i can think please help me

dy/dt= the rate of flow in - rate of flowing out

so flow in is 2/5 litre alcohol says the question and flow out is 2y(t)?

so dy/dt+2y(t)=2/5?
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May 30th, 2012, 07:18 AM   #7
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Re: help me, differential equation

See this topic.

Apparently someone is studying from the same book you are.
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May 30th, 2012, 11:37 AM   #8
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Re: help me, differential equation

i tried but my work is very big confusion can u show me steps to do part a.b.c
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May 30th, 2012, 12:13 PM   #9
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Re: help me, differential equation

a) Let V be measured in liters and t be measured in minutes. We are given the IVP:

where

Hence, we have:





We may now use the given initial condition to determine C:

thus:



b) Let A be measured also in liters. We are given:

where

Write the ODE in standard linear form:



c) Now we compute the integrating factor:



Multiplying the ODE by the integrating factor gives:











We may now use the given initial condition to determine C:



thus:

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