Question: In Problems x = c 1 cos t + c 2 sin t is a two-parameter family of solutions of the second order DE ''

In Problems x = c₁ cos t + c₂ sin t is a two-parameter family of solutions of the second order DE '' + x = 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.

1. x(0) = -1, x'(0) = 8

2. x(π/2) = 0, x'(π/2) = 1

3. x(π/6) = ½, x'(π/6) = 0

4. x(π/4) = √2, x'(π/4) = 2√2

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