Question

Problem 4 ( 14 points) (a) 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. (t +3)(t - 5)/" + 3ty' + 4y = 2, y(3) = 0, y(3) = -1. (b) Find the Wrongskian of two solutions of the following equation without solving the equation. (t2 – 1)y" – (t – 1)(t + 1)(t + 2)y' + (t + 2)y = 0.

Answer 1

4(ar. The ode can be written as yoll + a Ct). y7. bby = f(ty, .. where alt= 3 2 2 2 2 (E-53 blo 2 L 03 (457 4 fly 12,4-2,

we see that t=-34 t=5 ase the fingulas points of the ode.. - -3 's' how the longest internal of the existance of the folutian of the ode is the largest radious of Convergence of the power series Jocution about X=3, which is (1,5). 46 vi(t)= cexp. Ef attrat). = ci exp. ((((i (te) da) = c exh Jt+2) dt = e. exp. (6% + 2 t). ť! is the worong kian of the given lymatian.