Given an ODE of the form

a regular singular point

is one such that

or

diverge as

, but the limits of

and

as

exist.
We have for

,

and as

, we have

and

, so indeed

is a regular singular point.
We then look for a series solution about the regular singular point

of the form

Substituting into the ODE gives




From this we find the indicial equation to be

Taking

, and in the

term above we find

. So we have

Since

, all coefficients with an odd index will also vanish.
So the first three terms of the series expansion of this solution are

with

,

, and

.
Answer:
The answer is (-4,9)
Step-by-step explanation:
When you reflect across y=-x the x and y coordinates switch places and change signs.
Answer:
x = 10
Step-by-step explanation:
Use CPCTC (Corresponding parts of congruent triangles are congruent).
Set the ratios:

First, simplify. Combine like terms:

Next, cross multiply.

Isolate the variable, x. Divide 6.5 from both sides of the equation:

Check:

Plug in 10 for x (Your answer). Cross multiply, then simplify:



(True).
~
Answer:
n<-12
Step-by-step explanation:
4<-1/3n
4<-n/3
4×3<-n
12<-n
-12<n
n<-12
Answer:
You can either do a back to back stem and leaf plot, where you would have double the values. In a normal stem and leaf plot you would just have one set of 3's where you would put all the values that start with 3 in that column. A back to back is the same but instead you would have two 3 values, where anything that is higher than 5 would be in the second value of 3, but anything lower would be in that first value of 3.