Question: In Problems y = c 1 cos 2x + c 2 sin 2x is a two paramet4er family of solutions of the second order DE

In Problems y = c₁ cos 2x + c₂ sin 2x is a two paramet4er family of solutions of the second order DE y'' + 4y = 0. If possible, find a solution of the differential equation that satisfies the given side conditions The condition specified at two different points are called boundary conditions.

1. y(0) = 0, y(π/4) = 3

2. y(0) = 0, y' (π) = 0

3. y'(0) = 0, y' (π/6) = 0

4. y(0) = 1, y'(π) = 5

5. y(0) = 0, y(π) = 2

6. y'(π/2) = 0, y'(π) = 0

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1 From the boundary conditions y0 0 and y4 3 we obtain y0 c 1 0 Thus c 1 0 c 2 3 and the solution ... View full answer

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