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6. 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. 2 (a) et x" + In(t2 - 1) x' + In((1 -t)2) x = V4-t2 i. x(0) = 1, x(0) =1 ii. x = 1 x' NICO NICO =1 iii. x (-2) = 1 x (-2) =1 dy 1 dy (b) In(a) da-3 tan (7 x) = V2 - x2 dx 1 1 i. y 10 = 0.1, y' 10 = 0.2, y" 10 = 0.5 6 10 = 1.1, y' 6 ii. y 10 = 0.9, 2" (10 = 0.4 t (c) 1 2+ 3 p" = e (p+1) i. p(to) = 0, p'(to) = 1 where to E R is given