Program Explanation Given information: Given differential equations with two initial conditions d v d t = − ( 0.04 ) v − 9.8 , v ( 0 ) = 49 Explanation : The solution to the initial value problem can be found by applying the iterative formula for Euler’s method given by y n + 1 = y n + h f ( x n , y n ) , where h is the step size. t n = 50 n = 100 a c t u a l ( v ) 0 49.0000 49.0000 49.0000 1 37.4722 37.4721 37.4721 2 26.3964 26.3963 26.3962 3 15.7549 15.7547 15.7546 4 5.5307 5.5304 5.5303 5 − 4.2926 − 4.2930 − 4.2932 6 − 13.7308 − 13.7313 − 13.7314 7 − 22.7989 − 22.7994 − 22.7996 8 − 31.5115 − 31.5120 − 31.5122 9 − 39.8824 − 39.8830 − 39.8832 10 − 47.9251 − 47.9257 − 47.9259 We notice first that the two columns agree to 3 decimal places (each difference being than 0

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Linear Programming Concepts

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Chapter 2.5, Problem 29P

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Use the improved Euler’s method to approximate v (t) using both n=50 and n=100 subintervals. Display the results at intervals of 2 second. Do the two approximations each rounded to two decimal places agree both with each other and with the exact solution.

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Chapter 2.5, Problem 28P

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Use the improved Euler’s method to approximate v (t) using both n=50 and n=100 subintervals. Display the results at intervals of 2 second. Do the two approximations each rounded to two decimal places agree both with each other and with the exact solution.

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Use the improved Euler’s method to approximate v (t) using both n=50 and n=100 subintervals. Display the results at intervals of 2 second. Do the two approximations each rounded to two decimal places agree both with each other and with the exact solution.

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