7. Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution. (i) (t 1)y" 3ty + 4y = sint, y(-2) = 2, y'(-2) = 1 (ii) t(t 4)y" +3ty' + 4y = 2, y(3) = 0, y'(3) = -1 (iii) (x-2)y"+y+ (x-2)(tan x)y = 0, y(3) = 1, y'(3) = 2. 8. Find the Wronskian of the given pair of functions: (i) cost, sint (ii) 0, e² sint (iii) r, ret (iv) cos20, 1+ cos 20.