Determine the singular points of the given differential equation. Classify each singular point as regular or irregular. (Enter your answers as a comma-separated list. Include both real and complex singular points. If there are no singular points in a certain category, enter NONE.)(x2 − 4)2y'' + (x + 2)y' + 7y = 0

Answers

Answer 1

Answer:

Step-by-step explanation:

Given that:

The differential equation; [tex](x^2-4)^2y'' + (x + 2)y' + 7y = 0[/tex]

The above equation can be better expressed as:

[tex]y'' + \dfrac{(x+2)}{(x^2-4)^2} \ y'+ \dfrac{7}{(x^2- 4)^2} \ y=0[/tex]

The pattern of the normalized differential equation can be represented as:

y'' + p(x)y' + q(x) y = 0

This implies that:

[tex]p(x) = \dfrac{(x+2)}{(x^2-4)^2} \[/tex]

[tex]p(x) = \dfrac{(x+2)}{(x+2)^2 (x-2)^2} \[/tex]

[tex]p(x) = \dfrac{1}{(x+2)(x-2)^2}[/tex]

Also;

[tex]q(x) = \dfrac{7}{(x^2-4)^2}[/tex]

[tex]q(x) = \dfrac{7}{(x+2)^2(x-2)^2}[/tex]

From p(x) and q(x); we will realize that the zeroes of (x+2)(x-2)² = ±2

When x = - 2

[tex]\lim \limits_{x \to-2} (x+ 2) p(x) = \lim \limits_{x \to2} (x+ 2) \dfrac{1}{(x+2)(x-2)^2}[/tex]

[tex]\implies \lim \limits_{x \to2} \dfrac{1}{(x-2)^2}[/tex]

[tex]\implies \dfrac{1}{16}[/tex]

[tex]\lim \limits_{x \to-2} (x+ 2)^2 q(x) = \lim \limits_{x \to2} (x+ 2)^2 \dfrac{7}{(x+2)^2(x-2)^2}[/tex]

[tex]\implies \lim \limits_{x \to2} \dfrac{7}{(x-2)^2}[/tex]

[tex]\implies \dfrac{7}{16}[/tex]

Hence, one (1) of them is non-analytical at x = 2.

Thus, x = 2 is an irregular singular point.


Related Questions

Function or not a function


-3 6

5 6

3 -2

-5 1

Answers

Answer: It is a function.

Step-by-step explanation:

A function is a relation between two sets that associates every element of the one set to exactly one element of the other set.

Given table :  Input values    Output values

                             -3                         6

                                5                        6

                                  3                      -2

                                 -5                         1

Here each input value value is related to exactly one out out value.

Hence, it is a function.

can you please help me with this question ​

Answers

7 guests
It costs 5 dollars per guest, so divide 35 by 5
7 guest, and 5 dollers a guest

Think about Digit's game of spinning the spinner.

He wants to know the probability of the following events happening on two separate spins.

A: spinning praline wafer

B: spinning oven-baked apple & lavender calzone

Which formula should Digit use to find the probability?

P(A∩B)=P(A)⋅P(B|A)
P(A∪B)=P(A)+P(B)
P(A∪B)=P(A)+P(B)−P(A∩B)
P(A∩B)=P(A)⋅P(B)

Answers

Answer:

Should be P(A∩B)=P(A)⋅P(B)

Can anyone help me determine the next terms in these sequences?
6, 8, ?, 16, 24, 28,...
1000, 999, 996, 991, 984,...
7, 9, 13, 17, ?, 29,...
8, 11, 29, 51, 125, ?, 293,...
9, 11, 30, 51, 126, ?, 294,...
102532, 112433, 122334,...

Answers

Answer:

132235

Step-by-step explanation:

if Brian is 24 years old and his sister is 16 years old. how old is Brian to his sister.

and if Brian's mother is 56 years old how is his mother to his sister. if

Brian's mother is 56 how old is his mother to his sister.

if their father is 63 how old is he to the mother Brian's mother and Brian.
is the mother related to the sister. how old is the sister to the mother and the father. band uncle is 84 how old is he to Brian's mother sister father and to himself. last question how old is other ages add together. who is the oldest​

Answers

Answer:

1. 3:2

2. 7:2

3. 63:56:24

4. 16:56:63

5. 84:56:16:63

the ages added up is 219

the uncle is the oldest

Step-by-step explanation:

I'm answering by ratios because I'm not exactly sure what you mean.

24:16 = 6:4 = 3:2

56:16 = 7:2

63:56:24 is already in its simplest form I think??

16:56:63  also in its simplest form

84:56:16:63

the ages added up is 219

the uncle is the oldest

Plot the x- and y- intercepts to graph the equation.

y= -1/2x - 3

Answers

Step-by-step explanation:

work is shown and pictured

Louis age is three years more than twice the age of Sánchez . The sun of their ages is 39. How old are Sánchez and Louis ?

Answers

Answer:

Sanchez- 42

Louis- 40

Step-by-step explanation:

hope this helps

If you invest $2,000 now at an interest rate of 5% compounded quarterly, in 20 years the investment will be worth?

Answers

Answer:

it would be worth 80,000

Step-by-step explanation:

Brainliest to right answer

Answers

Answer:

the answer is A)no solutions

4. Which pair of trig functions are equivalent?
sin 23, sin 67
COS 41, sin 41
cos 58, sin 122
cos 76, sin 14

Answers

cos 76, sin 14

The cos and sin have to add to 90°

The pair of trigonometric functions that are equivalent is cos76°, sin14°.

What are trigonometric ratios in terms of a right-angle triangle?

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

We know sin(π/2 - Ф) = cosФ and cos(π/2 - Ф) = sinФ.

sin23° = cos(90° - 23°) = cos67°.

cos41° ≠ sin41°.

cos58° = cos(180° - 58°) = cos122°.

cos76° = sin(90° - 76°) = sin14°.

learn more about trigonometric functions here :

https://brainly.com/question/6904750

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30. What is the degree of the polynomial?

31. Which polynomial is in descending order in terms of x?

Picture attached

Answers

Answer:

Step-by-step explanation:

30). [tex]5^{th}[/tex] degree ( 4 + 1 = 5 ; 1 + 1 = 2 and 2 + 2 = 4 )

31) D) Choice D

Which of the following statements is true of the system below?
-2x-3y=-1
3x+6y=0

A. The solution to this system is (3,-2).
B. The solution to this system is (2,-1).
C. This system has no solutions.
D. This system has infinitely many solutions.

Answers

Answer:

y=mx+b 57+cb

Step-by-step explanation:

Answer:

b. the solution to this system is (2,-1)

Step-by-step explanation:

solve for h h and 26 is −52

Answers

Answer:

If you mean h multiplied by 26 is -52 then h is -2

If it is added to 26 then h is -78

If it is subtracted then h is -26

Step-by-step explanation:

answer this please i appreciate it

Answers

Answer:

oh I know the answer its r=27

Step-by-step explanation:

I know that it is 27 because 16+24=65 and 65+27 is 180

10/16 reduced to the lowest term?

Answers

5/8 is the lowest term

A bike costs $520. You have a coupon for 25% off.
Find the discount amount and sale price.

Answers

Answer:

Discount: $130

Sale price: $390

Step-by-step explanation:

Discount:   0.25 * $520 = $130

Sale price:

   bike cost - discount = sale price

   $520 - $130 = $390

Zoey invested $230 in an account paying an interest rate of 6.3% compounded daily.
Assuming no deposits or withdrawals are made, how much money, to the nearest
hundred dollars, would be in the account after 12 years?

Answers

Answer:

A ≈ $500

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Algebra I

Compounded Interest Rate: A = P(1 + r/n)ⁿˣ

A is final amountP is initial (principle) amountr is raten is number of compoundsx is number of years

Step-by-step explanation:

Step 1: Define

P = 230

r = 0.063

n = 365

x = 12

Step 2: Solve for A

Substitute:                    A = 230(1 + 0.063/365)³⁶⁵⁽¹²⁾Divide:                          A = 230(1 + 0.000173)³⁶⁵⁽¹²⁾Multiply:                        A = 230(1 + 0.000173)⁴³⁸⁰Add:                              A = 230(1.00017)⁴³⁸⁰Exponents:                   A = 230(2.1296)Multiply:                        A = 489.808

Help me out here please....

Answers

4 because when it’s all added up

5
I
А
Given: AC bisects ZBAD
and ZBCAZDCA
D
Prove: AABC = AADC
B
с
Statement
Reason

Answers

Answer:

6

Step-by-step explanation:

The segment AC is the angle bisector of angle BAD and angle BCD.

What is an angle bisector?

A ray, segment, or line that divides a given angle into two equal angles is known as an angle bisector.

When something is bisected or bisected, it is split into two equal sections. In geometry, an angle bisector is a line or ray that divides a triangle into two equal angles.

here, we have,

Given that ΔABC ≅ ΔADC Prove: AC bisects ∠BAD and AC bisects ∠BCD​

From the given data it is concluded that all the corresponding angles of the triangle are equal to each other.

In the triangle ABC and ADC:-

∠BAC = ∠DAC

∠BCA = ∠DCA

From the above proof, it is concluded that the AC bisects ∠BAD and ∠BCD.

Therefore, the segment AC is the angle bisector of angle BAD and angle BCD.

To know more about an angle bisector follow

brainly.com/question/24677341

#SPJ7

At the grocery store, sliced turkey deli meat is on sale for $11 for 2 pounds. a. What is the cost per pound of sliced turkey deli meat? b. Write an equation to represent the cost "y" of sliced turkey deli meat measured in "x" pounds. *

Answers

Answer:

- $5.5 per pound

- [tex]y = 5.5x[/tex]

Step-by-step explanation:

Given

$11 for 2 pounds

Solving (a): Cost per pound

This is calculated by dividing $11 by 2 pounds

[tex]Cost\ per\ pound = \frac{\$11}{2\ lb}[/tex]

[tex]Cost\ per\ pound = \$5.5/\ lb[/tex]

Hence, the cost per pound is $5.5 per pound

Solving (b): Represent as an equation.

If 1 pound costs $5.5 (as shown in (a))

Then

x pounds costs $5.5 * x

[tex]Cost = 5.5 * x[/tex]

[tex]Cost = 5.5x[/tex]

This cost is represented with y

[tex]y = 5.5x[/tex]

2 4/5 ___ 2.45
(>,<,=)

Answers

Answer:

2 and 4/5 > 2.45

Step-by-step explanation:

2.8 is greater than 2.45

Answer:

2 4/5 is equal to 2.8 so 2 4/5 > 2.45

Step-by-step explanation:

Complete the statement for triangle HJK with medians (HN), (JL), and (KM), and centroid P. PN = ____ HN *
1 point
1/2
2
1/3
2/3

Answers

Answer:

Step-by-step explanation:

PN = [tex]\frac{1}{3}[/tex] HN

Which polynomial is paired to its factored form?

49x2 + 112x + 64 and (7x + 8)3
25x2 − 45x + 81 and (5x – 9)2
216x3 − 540x2 + 450x – 125 and (6x – 5)3
729x3 + 324x2 + 144x + 64 and (9x + 4)3

Answers

Answer:

216 x^3 - 540 x^2 + 450 x - 125 = (6 x - 5)^3

Step-by-step explanation:

The first one cannot be a perfect cube, since the first term contains x^2 and not x^3.

the second one is not a perfect square (the coefficient of the middle term should be an even number: "-90")

The third expression is the perfect cube as shown.

two angles of a triangle measure 55° and 20°

Answers

Answer: All triangles have a 180 degree to them so 55+20 is 75 AND 180 degrees - 75 gives us 105 degrees. Although I know my math is correct a picture of this triangle would be helpful

Step-by-step explanation:

Dave ran from one corner of a field to the opposite corner , a distance of 100 meters . Then he ran along its length, a distance of 96 meters . How wide is the field

Answers

Answer:

28 meters wide

Step-by-step explanation:

This involves using the Pythagorean Theorem.

We know: a (the length)=96, b (the width)=?, c (diagonal distance)=100

a^2+b^2=c^2

96^2+b^2=100^2

9216+b^2=10000

b^2=784

b=28

The field is 28 meters wide

WRITE THE POINT -SLOPE FORM OF THE EQUATION OF THE LINE THAT PASSES THROUGH THE POINTS (5,9) AND (-6,10)

Answers

Answer:

y-5 = -3(x-9)

Step-by-step explanation:

(9--6)/ (5-10)

(9+6)/ (5-10)

15/-5

-15/5

Slope = -3

y-y1 = m(x - x1)

y-5 = -3(x - 9)

Which of the following is the least expensive cereal per ounce 13oz for 2.59 11.4 oz for 3.69 12oz for 3.99 20 oz for 5.99

Answers

Answer:

13 oz for 2.59 (im pretty sure)

Step-by-step explanation:

13 divided by 2.59 means every 5.01393 ounce it costs 1$. and from there you just find how many ounces compared to dollars.

Multiply.

−2 1/4X(−2 1/3)


−5 1/4

−41 1/2

41 1/2

5 1/4

Answers

The result of [tex]\tt{} - 2 \frac{1}{4} \times ( - 2 \frac{1}{3} )[/tex] is [tex]\tt{}5 \frac{1 }{4} [/tex]

preliminary

Pecahan dalam matematika adalah bilangan rasional yang dapat ditulis dalam bentuk [tex]\tt{}\frac{x}{y}[/tex] (dibaca x per y), dengan bentuk dimana x dan y merupakan bilangan bulat, y tidak sama dengan 0, dan bilangan x bukan kelipatan bilangan y.

Explanation

[tex]\tt{}- 2 \frac{1}{4} \times ( - 2\frac{1}{3} )[/tex]

[tex]\tt{} - \frac{9}{4} \times ( - \frac{7}{3} )[/tex]

[tex]\tt{}\frac{3}{4} \times 7[/tex]

[tex]\tt{}\frac{3 \times 7}{4} [/tex]

[tex]\tt{} \frac{31}{4} [/tex]

[tex]\tt{}5 \frac{1}{4} [/tex]

find the GCF of the ​

Answers

Answer:

6x

Step-by-step explanation:

24 and 30 share a GCF of 6. x^2 and x^2y share a GCF of x as we do not know what the value of y is.

Answer:

6xxxxxxxxxxxxxxxx with one x

There are 13 left-handed and 21 right-handed spirals on the cacti in the photograph. What is special about these numbers?
A. The value of the 13th term of the pyramidal sequence is 21.
B. They are consecutive terms in the pyramidal sequence.
C. The value of the 13th term of the Fibonacci sequence is 21.
D. They are consecutive terms in the Fibonacci sequence.

THE CORRECT ANSWER IS D!

Answers

Answer: D. They are consecutive terms in the Fibonacci sequence.

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