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6 Jan 2022
y' = y + sin (x) y' = x + sin (y) y' + y = e^t y' + y^3 = e^t Use Euler's method for each of the following. If more than 5 steps are require computer or calculator. If an exact solution is possible, find it, and calculate the Euler's method. Given that y' = 3y - 100t and y(0) = 10, estimate y(1) using delta t = 0.25. Given that y' = 3y - 100t and y(0) = 10, estimate y(1) using delta t = 0.01. Given that y' = 3y(1 - y/100) - 100t and y(0) = 10, estimate y(1) using delta t = 0.25. Given that y' = 3y(1 - y/100) - 100t and y(0) = 10, estimate y(1) using delta t = 0.01. Create slope fields as directed for each of the following DE's. Sketch in a curves based on the slope field. If more than 10 slope marks are required, use or calculator. What can you say about the long term behavior of the different (what happens for various initial conditions)? DE is y' = -2y, using integer values of the variables for 0 lessthanorequalto x lessthanorequalto 2 and -1 lessthanorequalto y DE is y' = -2x, using integer values of the variables for 0 lessthanorequalto x lessthanorequalto 2 and -1 lessthanorequalto DE is y' = y(1 - y) for -1 lessthanorequalto x lessthanorequalto 5 and -1 lessthanorequalto y lessthanorequalto 2 using a 15 by 15 grid or
y' = y + sin (x) y' = x + sin (y) y' + y = e^t y' + y^3 = e^t Use Euler's method for each of the following. If more than 5 steps are require computer or calculator. If an exact solution is possible, find it, and calculate the Euler's method. Given that y' = 3y - 100t and y(0) = 10, estimate y(1) using delta t = 0.25. Given that y' = 3y - 100t and y(0) = 10, estimate y(1) using delta t = 0.01. Given that y' = 3y(1 - y/100) - 100t and y(0) = 10, estimate y(1) using delta t = 0.25. Given that y' = 3y(1 - y/100) - 100t and y(0) = 10, estimate y(1) using delta t = 0.01. Create slope fields as directed for each of the following DE's. Sketch in a curves based on the slope field. If more than 10 slope marks are required, use or calculator. What can you say about the long term behavior of the different (what happens for various initial conditions)? DE is y' = -2y, using integer values of the variables for 0 lessthanorequalto x lessthanorequalto 2 and -1 lessthanorequalto y DE is y' = -2x, using integer values of the variables for 0 lessthanorequalto x lessthanorequalto 2 and -1 lessthanorequalto DE is y' = y(1 - y) for -1 lessthanorequalto x lessthanorequalto 5 and -1 lessthanorequalto y lessthanorequalto 2 using a 15 by 15 grid or
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10 Jan 2022
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