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Task 1 (Spec 2.f). Solve the following systems of linear differential equations with the initial values pro- vided. I=-2x+5y y = x - 2y x(0)=1 y(0) = 2 T=3x-.25y y=x+2y (0) 0 y(0) = 1

Task 1 (Spec 2.f). Solve the following systems of linear differential equations with the initial values pro- vided. I=-2x+5y y = x - 2y x(0)=1 y(0) = 2 T=3x-.25y y=x+2y (0) 0 y(0) = 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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MAT-3304 Due Due: October 3, 2022 30 3 1/1 x(0) = 1 y(0) = 2 9 x = -2x + 5y y = x - 2y F4 Specification Problems Task 1 (Spec 2.f). Solve the following systems of linear differential equations with the initial values pro- vided. Commented Problems Math Competitions DIFFERENTIAL EQUATIONS 100% + HomeWork # 06 0 F5 Task 2 (Spec 3.c). Formulate a linear system of differential equations for the following initial value problem. It is a non-homogenous system of differential equations but start by solving the homogenous version and then adding constants to the solutions until you have matched the non-homogenous parts as well. There are two tanks, Tank A and Tank B. They have capacities of 2500 L and 15000 L respec- tively. Into Tank A there is a 25 L/min flow of water containing .1kg/L of Red Dye Number 5. There a flow of 25L/min of water from Tank A to Tank B. There is a return flow of 15 L/min from Tank B to Tank A. There is a outflow from Tank B that keeps both tanks full without otherwise overflowing. Tank A starts with .17 kg/L of Red Dye Number 5 in it. Tank B starts clean. What are the concentrations of Red Dye Number 5 in both tanks at time t? Task 3 (Spec 3.d). Take your solutions to Task 2. Graph them and use them to give a physical inter- pretation of the concentrations of Red Dye Number 5 in the two tanks. Use them to estimate the time it takes until the two tanks are within 5% of the their equilibrium concentrations. Give an account of how physically reasonable the time and solutions you got were. Last Revision Possible: 24 October, 2022 MacBook Air F6 T= 3x - 25y y = x + 2y (0) = 0 y(0) = 1 O Fall 2022 September 27, 2022 F7 DII F8 F9 F1
Transcribed Image Text:MAT-3304 Due Due: October 3, 2022 30 3 1/1 x(0) = 1 y(0) = 2 9 x = -2x + 5y y = x - 2y F4 Specification Problems Task 1 (Spec 2.f). Solve the following systems of linear differential equations with the initial values pro- vided. Commented Problems Math Competitions DIFFERENTIAL EQUATIONS 100% + HomeWork # 06 0 F5 Task 2 (Spec 3.c). Formulate a linear system of differential equations for the following initial value problem. It is a non-homogenous system of differential equations but start by solving the homogenous version and then adding constants to the solutions until you have matched the non-homogenous parts as well. There are two tanks, Tank A and Tank B. They have capacities of 2500 L and 15000 L respec- tively. Into Tank A there is a 25 L/min flow of water containing .1kg/L of Red Dye Number 5. There a flow of 25L/min of water from Tank A to Tank B. There is a return flow of 15 L/min from Tank B to Tank A. There is a outflow from Tank B that keeps both tanks full without otherwise overflowing. Tank A starts with .17 kg/L of Red Dye Number 5 in it. Tank B starts clean. What are the concentrations of Red Dye Number 5 in both tanks at time t? Task 3 (Spec 3.d). Take your solutions to Task 2. Graph them and use them to give a physical inter- pretation of the concentrations of Red Dye Number 5 in the two tanks. Use them to estimate the time it takes until the two tanks are within 5% of the their equilibrium concentrations. Give an account of how physically reasonable the time and solutions you got were. Last Revision Possible: 24 October, 2022 MacBook Air F6 T= 3x - 25y y = x + 2y (0) = 0 y(0) = 1 O Fall 2022 September 27, 2022 F7 DII F8 F9 F1
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