Question

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

Answer 1

Explanation:

Solve the linear system, X ′

=AX where A=( 1

1

​

5

−3

​

), and X=( x(t)

y(t)

​

) Give the general solution. c 1

​

( −1

1

​

)e 4t

+c 2

​

( 5

1

​

)e −2t

c 1

​

( 1

1

​

)e 4t

+c 2

​

( 5

−1

​

)e −2t

c 1

​

( 1

1

​

)e −4t

+c 2

​

( 5

−1

​

)e 2t

c 1

​

( −1

1

​

)e −4t

+c 2

​

( 5

1

​

)e 2t