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1) Find the solution of the given initial value problem and describe the behavior of the...

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Advance Math

1) Find the solution of the given initial value problem anddescribe the behavior of the solution as t ? +?

y" + 4y' + 3y = 0, y(0) = 2, y'(0) = ?1.

2) Find a differential equation whose general solution isY=c1e2t + c2e-3t

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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