Question

Find L{f(t)} where f(t) is deffned by tho piecevise-defined function, f(t)={ e −t

,
−1,
​
0≤t
t≥5
​
I{1}= s
1
​
L Lt}= s 2
1
​
L{t n
}= s n+1
n!
​
[{e at
⋅f(t)}=F(s−a) L {sinkt}= s 2
+k 2
k
​
L{coskt}= s 2
+k 2
s
​
∫{f(t−a)U(t−a)}=e −as
F(s) s+1
1−e −5s+5
​
− s
e −5s
​
s+1
1−e −5s−5
​
− s
e −5s
​
s−1
1+e 5s−5
​
+ s
e 5s
​
s+1
1−e −5s
​
+ s
e −5s
​

Answer 1

Explanation:

Let y=∑ n=0

[infinity]

​

c n

​

x n

. Substitute this expression into the following differential equation and simplify to find the recurrence relations. Select two answers that represent the complete recurrence relation. 2y ′

+xy=0 c 1

​

=0 c 1

​

=−c 0

​

c k+1

​

= 2(k−1)

c k−1

​

​

,k=0,1,2,⋯ c k+1

​

=− k+1

c k

​

​

,k=1,2,3,⋯ c 1

​

= 2

1

​

c 0

​

c k+1

​

=− 2(k+1)

c k−1

​

​

,k=1,2,3,⋯ c 0

​

=0