Question

(r 2

−2r+2) 2
r 2
(r−2) 3
=0 Write the nine fundamental solutions to the differential equation as functions of the variable t. y 1
=
y 4
=
y 7
=
y 2
=
y 5
=
y 8
=
y 3
=
y 6
=
y 9
=
(You can enter your answers in any order.)=

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