Question: 7. Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt

7. Determine the longest interval in which the given initial value problem

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,et sint (iii) x, (iv) cos0, 1+cos 20. Ie

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