Let y(t) satisfy the following 2nd order ordinary differential equation: 5y" - 2y+3y=-1, with initial conditions: y(0) = 7, y'(0) = 3. Let Y(s) represent the Laplace Transform of y(t). Then Y(s) can be represented as: (5s2 + bs + c)Y(s) = d +e+fs, S where b, c, d, e and f are constants. - The above equation for Y(s) may be rearranged to give: ps² + qs + r Y(s) = s(5s² + bs + c) where p, q and r are constants.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let y(t) satisfy the following 2nd order ordinary differential
equation:
5y" 2y+3y=-1,
with initial conditions: y(0) = 7, y'(0) = 3.
Let Y(s) represent the Laplace Transform of y(t) . Then Y(s) can
be represented as:
d
(582 + 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 + qs + r
s(5s² + bs + c)
where p, q and r are constants.
Y(s) =
=
I
Transcribed Image Text:Let y(t) satisfy the following 2nd order ordinary differential equation: 5y" 2y+3y=-1, with initial conditions: y(0) = 7, y'(0) = 3. Let Y(s) represent the Laplace Transform of y(t) . Then Y(s) can be represented as: d (582 + 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 + qs + r s(5s² + bs + c) where p, q and r are constants. Y(s) = = I
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