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Auxiliary equation

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1. Find y as a function of t if

y'' - 3y' - 18y = 0,
y(0) = 6,
y(1) = 8.

Remark: The initial conditions involve values at two points.

2. Find y as a function of t if

3y'' + 28y = 0,
y(0) = 8,
y'(0) = 5.

Note: This particular problem can not handle complex numbers, so write your answer in terms of sines and cosines, rather than using e to a complex power.

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Auxiliary equation help is given.

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