Apply the Laplace transform to the differential equation, and solve for
Y
(
s
)
\displaystyle {Y}{\left({s}\right)}
Y
(
s
)
. DO NOT solve the differential equation. Recall:
h
(
t
−
α
)
\displaystyle {h}{\left({t}-\alpha\right)}
h
(
t
−
α
)
is the unit step function shifted to the right
α
\displaystyle \alpha
α
units.
y
′
′
+
9
y
=
2
(
t
−
3
)
h
(
t
−
3
)
−
2
(
t
−
6
)
h
(
t
−
6
)
,
y
(
0
)
=
y
′
(
0
)
=
0
\displaystyle {y}{''}+{9}{y}={2}{\left({t}-{3}\right)}{h}{\left({t}-{3}\right)}-{2}{\left({t}-{6}\right)}{h}{\left({t}-{6}\right)},\quad{y}{\left({0}\right)}={y}'{\left({0}\right)}={0}
y
′′
+
9
y
=
2
(
t
−
3
)
h
(
t
−
3
)
−
2
(
t
−
6
)
h
(
t
−
6
)
,
y
(
0
)
=
y
′
(
0
)
=
0
Y
(
s
)
\displaystyle {Y}{\left({s}\right)}
Y
(
s
)
=
Preview
Question 6
Submit
Try a similar question
License
[more..]
\displaystyle
Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question