When solving the differential equation
d2θ
dt2 − 6
dθ
dt − 10θ = 20 − e2t by Laplace
transforms, for given boundary conditions,
the following expression for L{θ} results:
L{θ} =
4s3 − 39/2
s^2 + 42s − 40
s(s − 2)(s^2 − 6s + 10)
Show that the expression can be resolved into
partial fractions to give:
L{θ} =
2
s − 1
2(s − 2) +
5s − 3
2(s2 − 6s + 10)
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