Partial fractions 19
4.
x 3 + 4x 2 + 20x − 7
(x − 1) 2 (x 2 + 8)
3
(x − 1)
+
2
(x − 1) 2 +
1 − 2x
(x 2 + 8)
5. When solving the differential equation
d 2 θ
dt 2 − 6
dθ
dt
− 10θ = 20 − e
2t
by Laplace
transforms, for given boundary conditions, the
following expression for L{θ} results:
L{θ} =
4s
3
−
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(s 2 − 6s + 10)
4.
x 3 + 4x 2 + 20x − 7
(x − 1) 2 (x 2 + 8)
3
(x − 1)
+
2
(x − 1) 2 +
1 − 2x
(x 2 + 8)
5. When solving the differential equation
d 2 θ
dt 2 − 6
dθ
dt
− 10θ = 20 − e
2t
by Laplace
transforms, for given boundary conditions, the
following expression for L{θ} results:
L{θ} =
4s
3
−
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(s 2 − 6s + 10)