Obtain the general solution unless otherwise instructed. Use synthetic division in factoring the auxiliary equations. (a) (D^3 + D^2 − 16D − 16)y = 0 (b) (4D^3 + 12D^2 + 13D + 10)y = 0 (c) (4D^5 − 23D^3 − 33D^2 − 17D − 3)y = 0

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Obtain the general solution unless otherwise instructed. Use synthetic division in factoring the auxiliary equations. (a) (D^3 + D^2 − 16D − 16)y = 0 (b) (4D^3 + 12D^2 + 13D + 10)y = 0 (c) (4D^5 − 23D^3 − 33D^2 − 17D − 3)y = 0 (d) (D^4 + 6D^3 + 9D^2)y = 0; when x = 0, y = 0, y'=0, y''= 6, and as x → ∞, y' → 1. For this particular solution, find the value of y when x = 1.

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