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Mathematics Blue

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A person is trying to fill her new swimming pool for the first time. Water is flowing into the pool at a constant rate of 30 liters/min. Unfortunately there is a hole and a crack in the pool from which water is leaking. Water is leaking out of the hole at a rate proportional to the square of the amount of water currently in the pool while water is leaking out of the crack at a rate proportional to the amount of water currently in the pool. As it had rained the previous day, the pool already contained 20 liters of water before filling began. let t(mins) be the time since the person started filling the pool and let W(t) be the number of liters of water in the pool at time t. Write down but do not solve the differential equation for W(t) along with its initial condition.

Now, is this correct?, this is as far as I have gotten but I am not sure if this is right?

I put dw/dt in as 30t, because it is 30 liters/min the rate of flow into the pool.

I put dw/dt out as -kw^2 - pw, because it is the sqaure and the constant amount as the rate of the flow out of the pool.

So combining this, dw/dt is 30t - kw^2 - pw where w(0) = 20 as the initial condition.


Thank you for the help in advance.

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