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Question: for the differential equation a find the set of points...

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For the differential equation dy уз dt1+ t2

a) find the set of points (a, b) for which dy уз dt1+ t2 , y(a) = b satisfies the hypotheses of the existence theorem. Since 2-3 t is continuous for all the values of (t, y), (a, b) can be any point in the plane.

b) find the set of points (a, b)t for which dy уз dt1+ t2 , y(a) = b satisfies the hypotheses of the uniqueness theorem. rac{partial }{partial y}(rac{y^{rac{2}{3}}}{1+t^{2}})=rac{2}{3(1+t^{2})y^{rac{2}{3}}} is continuous for a ll the values of (t, y) except y = 0, (a, b) can be any point in the plane other than b = 0.

c) find two different solutions of dy уз dt1+ t2 , y(0) = 0

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