Let y(t) satisfy the following 2nd order ordinary differential equation: 4y" - 5y' - 2y = -6, with initial conditions: y(0) = -1, y'(0) = 2. Let Y(s) represent the Laplace Transform of y(t). Then Y(s) can be represented as: d (4s²+bs + c)Y(s) = S where b, c, d, e and f are constants. + e + fs, The above equation for Y(s) may be rearranged to give: ps²+gs+r Y(s) = s(48²+bs + c) where p, q and r are constants. 1

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let y(t) satisfy the following 2nd order ordinary differential equation:
4y" — 5y' – 2y = −6,
-
with initial conditions:
y(0) = -1, y'(0) = 2.
I
Let Y(s) represent the Laplace Transform of y(t). Then Y(s) can be represented as:
d
(4s² + bs + c)Y(s) == + e + fs,
S
where b, c, d, e and f are constants.
The above equation for Y(s) may be rearranged to give:
ps²+gs+r
Y(s) =
s(48²+bs + c)
where p, q and r are constants.
Transcribed Image Text:Let y(t) satisfy the following 2nd order ordinary differential equation: 4y" — 5y' – 2y = −6, - with initial conditions: y(0) = -1, y'(0) = 2. I Let Y(s) represent the Laplace Transform of y(t). Then Y(s) can be represented as: d (4s² + bs + c)Y(s) == + e + fs, S where b, c, d, e and f are constants. The above equation for Y(s) may be rearranged to give: ps²+gs+r Y(s) = s(48²+bs + c) where p, q and r are constants.
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