We want a solution in the form

with derivatives


Substituting  and its derivatives into the ODE,
 and its derivatives into the ODE,

gives

Shift the index on the second sum to have it start at  :
:

and take the first term out of the other two sums. Then we can consolidate the sums into one that starts at  :
:
![\displaystyle(2a_2+2a_0)+\sum_{n\ge1}\bigg[(n+2)(n+1)a_{n+2}+(2-2n)a_n\bigg]x^n=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%282a_2%2B2a_0%29%2B%5Csum_%7Bn%5Cge1%7D%5Cbigg%5B%28n%2B2%29%28n%2B1%29a_%7Bn%2B2%7D%2B%282-2n%29a_n%5Cbigg%5Dx%5En%3D0)
and so the coefficients in the series solution are given by the recurrence,

or more simply, for  ,
,

Note the dependency between every other coefficient. Consider the two cases,
- If  , where , where is an integer, then is an integer, then





and so on, with the general pattern

- If  , then , then


and we would see that  for all
 for all  .
.
So we have
![y(x)=\displaystyle\sum_{k\ge0}\bigg[a_{2k}x^{2k}+a_{2k+1}x^{2k+1}\bigg]](https://tex.z-dn.net/?f=y%28x%29%3D%5Cdisplaystyle%5Csum_%7Bk%5Cge0%7D%5Cbigg%5Ba_%7B2k%7Dx%5E%7B2k%7D%2Ba_%7B2k%2B1%7Dx%5E%7B2k%2B1%7D%5Cbigg%5D)
so that one solution is

and the other is

I've attached a plot of the exact and series solutions below with  ,
,  , and
, and  to demonstrate that the series solution converges to the exact one.
 to demonstrate that the series solution converges to the exact one.
 
        
             
        
        
        
Answer:
53.3
Step-by-step explanation:
34^2=1156
41^2=1681
1156+1681=2837
Square root of 2837 is 53.26 which rounded to the nearest tenth is 53.3
 
        
             
        
        
        
Answer:
The probability that the pitcher throws exactly 8 strikes out of 15 pitches is approximately 0.199
Step-by-step explanation:
The given probability that the pitcher throws a strike, p = 0.507
The number of pitches thrown by the pitcher = 15 pitches
The probability that the pitcher does not throw a strike, q = 1 - P
∴  q = 1 - 0.507 = 0.493
By binomial theorem, we have;

When X = r =  8, and n = 15, we get;
The probability that the pitcher throws exactly 8 strikes out of 15 pitches, P(8), is given as follows
P(8) = ₁₅C₈ × 0.507⁸ × (1 - 0.507)⁽¹⁵ ⁻ ⁸⁾ = 6,435 × 0.507⁸ × 0.493⁷ ≈ 0.199
 
        
             
        
        
        
A squared + b squared = c squared
8.6^2+14.7^2=c^2
73.96+216.09=c^2
square root both sides and...
c=17.03085
Your answer is A
Hope this helps
        
             
        
        
        
Answer:
Arc ECG is the major arc
Step-by-step explanation:
Arc ECG is made by an angle which is greater than 180°.
All the other arcs listed are made by angles which are 180° or less than.
The greater the angle measure the greater the arc length.