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

1) Find the solution of the given initial value problem and describe 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 is Y=c₁e^2t + c₂e^-3t

3) 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(t − 4)y" + 3ty' + 4y = 2 = 0, y(3) = 0, y'(3) = −1.

4) Consider the ODE: y" + y' − 2y = 0. Find the fundamental set of solutions y1, y2 satisfying y1(0) = 1, y'1 (0) = 0, y2(0) = 0, y'2 (0) = 1.

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Expert Solution

Colby Messinger answered 1 year ago

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