#$&* course Phy 279 3/6 12 Query 13 Differential Equations*********************************************
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: Find the largest interval on which the equation t y '' + sin(2 t) / (t^2 - 9) y ' + 2 y = 0 has a solution, with the initial conditions y(1) = 0, y ' (1) = 1. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: t cannot equal 3 or -3 Interval is then -3
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: Tell whether each of the following is increasing or decreasing, and whether concave down or concave up, in the vicinity of the initial point: y '' + y = 2 - sin(t), y(0) = 1, y ' (0) = -1. y '' + y = - 2 t, y(0) = 1, y ' (0) = -1. y '' - y = t^2, y(0) = 1, y ' (0) = 1. y '' - y = - 2 cos(t), y(0) = 1, y ' (0) = 1. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: y '' + y = 2 - sin(t), y(0) = 1, y ' (0) = -1. o y(0) = 1 and y(0) = -1 o so it is decreasing at a increasing rate, concave down