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10 Nov 2019
2. (34 pts) Consider dxy (a) (4 pts) Print the slope field generated by Desmos, and sketch 4 solutions passing through (b) (4 pts) Using GeoGebra, print the slope field along with 4 solutions passing through (c) (6 pts) Using the Existence and Uniqueness Theorem for first-order DE (Picard's theo- (0,3), (0,-3), (0,0), and (4,2), respectively. (0,3), (0,-3), (0,0), and (4,2) rem), find all the points in the ry-plane for which the above differential equation is not guaranteed to have a solution using those initial conditions (d) (12 pts) For each initial condition, explain whether the Existence and U tells us whether a unique solution exists, and then use this information to explain what is happening for each of the four GeoGebra solutions. (e) (8 pts) Find the implicit solution and then the explicit solution to da(4)-2 What conic section is the implicit solution, and what is the domain of the explicit solu tion?
2. (34 pts) Consider dxy (a) (4 pts) Print the slope field generated by Desmos, and sketch 4 solutions passing through (b) (4 pts) Using GeoGebra, print the slope field along with 4 solutions passing through (c) (6 pts) Using the Existence and Uniqueness Theorem for first-order DE (Picard's theo- (0,3), (0,-3), (0,0), and (4,2), respectively. (0,3), (0,-3), (0,0), and (4,2) rem), find all the points in the ry-plane for which the above differential equation is not guaranteed to have a solution using those initial conditions (d) (12 pts) For each initial condition, explain whether the Existence and U tells us whether a unique solution exists, and then use this information to explain what is happening for each of the four GeoGebra solutions. (e) (8 pts) Find the implicit solution and then the explicit solution to da(4)-2 What conic section is the implicit solution, and what is the domain of the explicit solu tion?
Casey DurganLv2
13 Mar 2019