Problem A6. Consider the initial value problem 2y y(0) = 1. t-1' (a) Use Picard-Lidelöf (or its corollary) to show that

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Problem A6 Consider The Initial Value Problem 2y Y 0 1 T 1 A Use Picard Lidelof Or Its Corollary To Show That 1 (451.01 KiB) Viewed 34 times

Problem A6. Consider the initial value problem 2y y(0) = 1. t-1' (a) Use Picard-Lidelöf (or its corollary) to show that there is 6> 0 such that the IVP has a unique solution y : [−6, 6] → R. (b) Verify that for each c E R, y' = y(t) = [(t-1)² ift<1 c(t − 1)² if t≥1 is a solution to the IVP. Use part (b) to discuss the possible value of the ♂ > 0 from part (a).