3) Determine the longest interval in which the given initial value problem is certain to have...
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3) Determine the longest interval in which the given initialvalue problem is certain to have a unique twice-differentiablesolution. Do not attempt to find the solution t(t − 4)y\" + 3ty' +4y = 2 = 0, y(3) = 0, y'(3) = −1.
4) Consider the ODE: y\" + y' − 2y = 0. Find the fundamental setof solutions y1, y2 satisfying y1(0) = 1, y'1 (0) = 0, y2(0) = 0,y'2 (0) = 1.
3) Determine the longest interval in which the given initialvalue problem is certain to have a unique twice-differentiablesolution. Do not attempt to find the solution t(t − 4)y\" + 3ty' +4y = 2 = 0, y(3) = 0, y'(3) = −1.
4) Consider the ODE: y\" + y' − 2y = 0. Find the fundamental setof solutions y1, y2 satisfying y1(0) = 1, y'1 (0) = 0, y2(0) = 0,y'2 (0) = 1.
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