Problem A7. For yo ≥ 0, consider the IVP y' = 5t³y¹/5, y (0) (*) (a) Let yo > 0. Prove that there is 8 >0 so that (*) ha

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Problem A7 For Yo 0 Consider The Ivp Y 5t Y 5 Y 0 A Let Yo 0 Prove That There Is 8 0 So That Ha 1 (64.25 KiB) Viewed 28 times

(a) Let y0 > 0. Prove that there is δ > 0 so that (∗) hasa unique solution defined on [−δ, δ].
(b) Now, let y0 = 0. Show that y(t) = 0 for all t is a solutionto (∗). Then, use separation of variables to find another solutionto (∗).
(c) Is the function f(t, y) = 5t 3 y 1/5 Lipschitz in y on [0,1] × [0, 1]? Explain your answer.
Problem A7. For yo ≥ 0, consider the IVP y' = 5t³y¹/5, y (0) (*) (a) Let yo > 0. Prove that there is 8 >0 so that (*) has a unique solution defined on [-6, 6]. = yo. (b) Now, let 0. Show that y(t) Yo = use separation of variables to find another solution to (*). = 0 for all t is a solution to (*). Then, (c) Is the function f(t, y) = 5t³y¹/5 Lipschitz in y on [0, 1] × [0, 1]? Explain your answer.