1. For the following IVPs determine if the IVP has a unique solution; if it does, then determine the interval on which the unique solution exists for each IC given. (a) et a" + In(t2 - 1) a' + In((1 -t)2) x = V4-t2 i. x(0) = 1, x'(0) = 1 ii. x = 1 x = 1 iii. x (-2) = 1 x (-2) =1 (b) In(ac) dy 1 dy - tan(7 x) = da-3 V2 - x2 dx 1 i. y = 0.1, y' = 0.2, y" = 0.5 10 10 10 6 6 ii. y = 1.1, y' = 0.9, y" = 0.4 10 10 10 (c) (t - 1) p" - 3tp' + 4p = t(t -1) , p(-2) = 2, p'(-2) = 1 where to E R is given