Differential Equations Quiz
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LAPLACE TRANSFORMS
Question 1
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Find the Laplace transform of the function
f
(
t
)
=
cos
(
2
t
)
(
u
π
/
2
(
t
)
−
u
3
π
/
2
(
t
)
)
f(t) = \cos(2t)(u_{\pi/2}(t) - u_{3\pi/2}(t))
f
(
t
)
=
cos
(
2
t
)
(
u
π
/2
(
t
)
−
u
3
π
/2
(
t
))
.
A
s
s
2
+
4
(
e
−
π
s
/
2
−
e
−
3
π
s
/
2
)
\frac{s}{s^2+4}(e^{-\pi s/2} - e^{-3\pi s/2})
s
2
+
4
s
(
e
−
π
s
/2
−
e
−
3
π
s
/2
)
B
s
s
2
+
4
(
e
−
3
π
s
/
2
−
e
−
π
s
/
2
)
\frac{s}{s^2+4}(e^{-3\pi s/2} - e^{-\pi s/2})
s
2
+
4
s
(
e
−
3
π
s
/2
−
e
−
π
s
/2
)
C
s
s
2
+
4
(
e
−
π
s
/
2
+
e
−
3
π
s
/
2
)
\frac{s}{s^2+4}(e^{-\pi s/2} + e^{-3\pi s/2})
s
2
+
4
s
(
e
−
π
s
/2
+
e
−
3
π
s
/2
)
D
−
s
s
2
+
4
(
e
−
π
s
/
2
+
e
−
3
π
s
/
2
)
-\frac{s}{s^2+4}(e^{-\pi s/2} + e^{-3\pi s/2})
−
s
2
+
4
s
(
e
−
π
s
/2
+
e
−
3
π
s
/2
)
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