1st order differential equations

heyheyhey701

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Mar 12, 2011
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a 100-gallon is filled with pure water. salt water of concentration .1 pounds of sat per gallon of water is pumped into the tank at 25 gallons per minuet. brine leaves the tank at the same rate. let y(t) denote the amount of salt in the tank at time t. Set up and solve a first order differential equation for hte unknown function y(t) and compute teh amount of salt in the tank in the long run. Find y(infinity) = lim y(t) as t approaches infinity
 
\(\displaystyle \text{rate in}=(\frac{1}{10})(25)\)

\(\displaystyle \text{rate out}=\frac{y}{100}(25)\)

\(\displaystyle \frac{dy}{dt}=\text{rate in}-\text{rate out}\)

Now, set up the DE. Find your integrating factor.

Integrate to solve for y and use the initial condition t(0)=0 to solve for C.
 
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