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**Unformatted text preview: **AMATH 351 Homework 2 Section2.1 14,16,19,31,40 Section2.4 3,12,15,29 Section2.6 8,21,23,24 Section 2.1 In each of Problems 13 through 20 nd the solution of the given initial value problem. 14. y + 2 y = te- 2 t , y (1) = 0 16. y + (2 /t ) y = (cos t ) /t 2 , y ( π ) = 0 , t > 19. t 3 y + 4 t 2 y = e- t , y (- 1) = 0 , t < 31. Consider the initial value problem y- 3 2 y = 3 t + 2 e t , y (0) = y . Find the value of y that separates solutions that grow positively as t → ∞ from those that grow negatively. How does the solution that corresponds to this critical value of y behave as t → ∞ ? In Problem 40 use the method of Problem 38 to solve the given di erential equation. 40. y + (1 /t ) y = 3 cos 2 t, t > Section 2.4 In each of Problems 1 through 6 determine (without solving the problem) and interval in which the solution of the given initial value problem is certain to exist. 3. y + (tan t ) y = sin t, y ( π ) = 0 In each of Problems 7 through 12 state where in the ty-plane the hypotheses of...

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