[See Steps] (a) Verify that the hypothesis of the existence and uniqueness theorem are satisfied for the IVP for any t_0,y_0. y'=2y^2-4ty^2, y(t_0)=y_0 (1)
Question: (a) Verify that the hypothesis of the existence and uniqueness theorem are satisfied for the IVP for any \({{t}_{0}},{{y}_{0}}\).
\[y'=2{{y}^{2}}-4t{{y}^{2}},\,\,y\left( {{t}_{0}} \right)={{y}_{0}}\] (1)(b) Verify that for all values of the constant c
\[y\left( t \right)=\frac{1}{2{{t}^{2}}-2t+c}\]
is a solution to the IVP in equation 1.
(c) Does the above solution give all solutions to the IVP of equation 1?
Deliverable: Word Document 
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