Question

4. ∫ 0

2
​
e x
+ x 2
+1
1
​
dx 5. ∫ −5
−2
​
7e y
+ y
2
​
dy 6. ∫ 4
π
​
3
x
​
​
2sec 2
(w)−8csc(w)cot(w)dw

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