APPM 2360 Midterm: appm2360spring2013exam1_sol
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Suppose that where y0 is a real constant. dy dt. = (t 1)p|y|, y(0) = y0, (a) [5] consider y0 = 1. What does picard"s theorem allow you to conclude about the existence and/or uniqueness of a solution? (b) [5] consider y0 = 0. What does picard"s theorem allow you to conclude about the existence and/or uniqueness of a solution? (c) [5] let y0 = 4. Y f (t, y) = (t 1)p|y| (t, y) =( t 1. 2 y , y > 0 y < 0 are continuous in a neighborhood of the initial condition y(0) = y0. (a) for y0 = 1, both (1) and (2) are continuous. Therefore, picard"s theorem applies and says that there is one and only one solution. That is, the solution exists and is unique. (b) for y0 = 0, (1) is continuous, but (2) is not continuous.
