2. Mixing Problem A small swimming pool contains 100 L of pure water. A solution with...

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2. Mixing Problem A small swimming pool contains 100 L of pure water. A solution with a sodium bromide concentration of 0.4 kg/L is added at a rate of 5 L/min. (This helps treat for algae.) The solution is kept mixed and is drained from the pool at a rate of 3 L/min. What is the sodium bromide concentration after 20 minutes? 3. Euler's Method: Repeated Linear Approximation (a) Use Euler's method to approximate y(1), where y(x) is the solution of the initial-value problem for step sizes i. h = 1 ii. h = 0.5 dy +3xy = 6x2 y(0) = 3 dx (b) Find the solution for this initial value problem by solving explicitly. (c) Then find the error for each approximation (each step size) in part (a). How might you get less error? ur 2. Mixing Problem A small swimming pool contains 100 L of pure water. A solution with a sodium bromide concentration of 0.4 kg/L is added at a rate of 5 L/min. (This helps treat for algae.) The solution is kept mixed and is drained from the pool at a rate of 3 L/min. What is the sodium bromide concentration after 20 minutes? 3. Euler's Method: Repeated Linear Approximation (a) Use Euler's method to approximate y(1), where y(x) is the solution of the initial-value problem for step sizes i. h = 1 ii. h = 0.5 dy +3xy = 6x2 y(0) = 3 dx (b) Find the solution for this initial value problem by solving explicitly. (c) Then find the error for each approximation (each step size) in part (a). How might you get less error? ur