consider the differential equation xy''-xy' y=0. the indicial equation is r(r-1)=0. the recurrence relation is a series solution corresponding to the inndicial root r=0 is

Answers

Answer 1

The series solution for the differential equation xy'' - xy'y = 0, corresponding to the indicial root r = 0, is y(x) = a₀ + a₁x + a₂x² + a₃x³ + ...

To find the series solution corresponding to the indicial root r = 0 for the differential equation xy'' - xy'y = 0, we can use the method of Frobenius.

The indicial equation is given by r(r - 1) = 0, which has roots r = 0 and r = 1. We will focus on the root r = 0.

For the root r = 0, we assume a series solution of the form:

y(x) = Σ(aₙxⁿ)

Substituting this series into the differential equation, we can find the recurrence relation for the coefficients aₙ.

First, we differentiate y(x) with respect to x:

y'(x) = Σ(aₙn xⁿ⁻¹)

Next, we differentiate y'(x) with respect to x:

y''(x) = Σ(aₙn(n - 1) xⁿ⁻²)

Substituting these expressions into the differential equation, we get:

x(Σ(aₙn(n - 1) xⁿ⁻²)) - x(Σ(aₙn xⁿ⁻¹))(Σ(aₙxⁿ)) = 0

Expanding and reorganizing terms, we obtain:

Σ(aₙn(n - 1) xⁿ) - Σ(aₙn(n - 1) xⁿ) - Σ(aₙn xⁿ⁺¹) = 0

Simplifying, we have:

Σ(aₙn(n - 1) xⁿ) - Σ(aₙn(n - 1) xⁿ) - Σ(aₙn xⁿ⁺¹) = 0

Since this equation holds for all values of x, each term must vanish separately. Therefore, we can write the recurrence relation as:

aₙ(n(n - 1) - n(n - 1)) - aₙ₊₁ = 0

Simplifying, we get:

aₙ₊₁ = aₙ / (n(n - 1))

This recurrence relation allows us to compute the coefficients aₙ in terms of a₀.

Hence, the series solution for the differential equation xy'' - xy'y = 0, corresponding to the indicial root r = 0, is given by:

y(x) = a₀ + a₁x + a₂x² + a₃x³ + ...

where the coefficients aₙ can be determined using the recurrence relation aₙ₊₁ = aₙ / (n(n - 1)) with the initial condition a₀.

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Related Questions

find the 7th term of 4,5,6.25

Answers

Answer:

same i dont know just need points but good luck

Which statement is true about their work? Neither student solved for k correctly because K = 2 and StartFraction 1 over 8 EndFraction. Only Adler solved for k correctly because the inverse of addition is subtraction. Only Erika solved for k correctly because the opposite of One-half is Negative one-half. Both Adler and Erika solved for k correctly because either the addition property of equality or the subtraction property of equality can be used to solve for k.

Answers

Question:

Adler and Erika solved the same equation using the calculations below.

Adler’s Work

[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]

[tex]\frac{13}{8} - \frac{1}{2} = k + \frac{1}{2} -\frac{1}{2}[/tex]

[tex]\frac{9}{8}= k[/tex]

Erika’s Work

[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]

[tex]\frac{13}{8}+ (-\frac{1}{2}) = k + \frac{1}{2} + (-\frac{1}{2}).[/tex]

[tex]\frac{9}{8}= k[/tex]

Which statement is true about their work?

Answer:

Both Adler and Erika solved for k correctly because either the addition property of equality or the subtraction property of equality can be used to solve for k.

Step-by-step explanation:

Given

[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]

Required

What is true about Adler and Erika's workings

Analyzing Adler's work;

[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]

Adler subtracted 1/2 from both sides

[tex]\frac{13}{8} - \frac{1}{2} = k + \frac{1}{2} -\frac{1}{2}[/tex]

Solving the expression on the left-hand side

[tex]\frac{13}{8} - \frac{1}{2} = \frac{13 - 4}{8} = \frac{9}{8}[/tex]

Solving the expression on the right-hand side

[tex]k + \frac{1}{2} - \frac{1}{2} = k[/tex]

Hence:

[tex]\frac{9}{8}= k[/tex]

So, Adler's workings is correct

Analyzing Erika's work;

[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]

Erika added -1/2 to both sides

[tex]\frac{13}{8}+ (-\frac{1}{2}) = k + \frac{1}{2} + (-\frac{1}{2}).[/tex]

Solving the expression on the left-hand side

[tex]\frac{13}{8} + (-\frac{1}{2}) = \frac{13}{8} - \frac{1}{2} = \frac{13 - 4}{8} = \frac{9}{8}[/tex]

Solving the expression on the right-hand side

[tex]k + \frac{1}{2} + (-\frac{1}{2}) =k + \frac{1}{2} - \frac{1}{2} = k[/tex]

Hence:

[tex]\frac{9}{8}= k[/tex]

So, Erika's workings is correct

Both workings are correct

Answer: Both Adler and Erika are correct

Step-by-step explanation:

On Edge 2021

identify error GIVEN, bracelets - php200 necklaces php300 sales at least 3600 sells at most 50 pieces of bracelets and necklaces correct the errors​

Answers

hggggvv 666666666 hhggg 66

Which whole numbers does the square root of 69 falls in between?

Answers

The square root of 69 is approximately 8.3066, so it’s between 8 and 9.

Dado los puntos p1 (-7/2-9/2) y p2 (5/2, 3/2) calcular la representación gráfica, d p1 p2, pto medio de p1 p2, la pendiente (m) de la recta que pasa por medio de ellos. Porfavor ayúdenme la tarea es para el viernes y no entendió ​

Answers

Answer:

Ce clasă ești sa văd daca te pot ajuta

Find the sum. Write the sum as a mixed number, so the fractional part is less than 1. Number 3. 2 2/3 + 3 2/3 number 5. 9 3/6 + 2 2/6 number 7. 4 3/8 + 1 5/8

Answers

Answer:

See explanations below

Step-by-step explanation:

1)2 2/3 + 3 2/3

Convert to improper fraction

= 8/3 + 11/3

= (8+11)/3

= 19/3

= 6 1/3

hence the sum as mixed fraction is 6 1/3

2) 9 3/6 + 2 2/6

= 57/6 + 14/6

= (57+14)/6

= 71/6

= 11 5/6

Hence the value as a mixed fraction is 11 5/6

3) 4 3/8 + 1 5/8

= 35/8 + 13/8

= (35+13)/8

= 48/8

= 6

Hence the value is 6


Which is equivalent to b6/b2

Answers

Answer:

yuojsjsjskakavbhjsmsnnxjxj

please help, I really don't get this​

Answers

Answer:

-8, -8

Step-by-step explanation:

If you add the equations, you get -7x + 4x + 4y - 4y = 24. Canceling out the 4y and the -4y, and adding 4x to -7x, you get -3x = 24. Divide both sides by -3 and you get x = -8. Next, pick an equation and substitute x for -8. I am going to use the first equation. (-7)-8 + 4y = 24 is equal to 56 + 4y = 24. Subtract 56 from both sides to get 4y is equal to -32, and if you divide both sides by 4, you get y = -8.

9514 1404 393

Answer:

  (-8, -8)

Step-by-step explanation:

We notice that the coefficients of y are +4 and -4, so have a sum of zero. This means we can add the two equations to eliminate the y-terms.

  (-7x +4y) +(4x -4y) = (24) +(0)

  -3x = 24 . . . . . . . . . simplify

  x = -8 . . . . . . . . . . . divide both sides by -3

Now, we can find y using either equation.

  4(-8) -4y = 0

  -8 -y = 0 . . . . . . . . divide both sides by 4

  -8 = y . . . . . . . . . . add y to both sides

The solution to the system of equations is ...

  (x, y) = (-8, -8)

In order to conduct an experiment five subjects are randomly selected from a group of 48 subjects how many different groups of five subjects are possible

Answers

Answer:

1,712,304 ways

Step-by-step explanation:

This problem bothers on combination

Since we are to select 5 subjects from a pool of 48 subjects, the number of ways this can be done is expressed as;

48C5 = 48!/(48-5)!5!

48C5 = 48!/43!5!

48C5 = 48×47×46×45×44×43!/43!5!

48C5 = 48×47×46×45×44/5!

48C5 = 205,476,480/120

48C5 = 1,712,304

Hence this can be done in 1,712,304ways

WILL MARK BRAINLIEST PLS DO MY MATH DUE: 1 HOUR

Answers

1. a=9 2. k=0 3. w=3 4. x= 5 5. v=14 6. f=8 7. u=5 8. c=1 9. s=8 10. q=1/7 11. k= 1/5 12. j=9 13. r=120 14. b=1.4 15. g= 3.1 and 16. m=25

I also post a picture on how I got each answer.

Hope this helped you out

Answer:

a=9 2. k=0 3. w=3 4. x= 5 5. v=14 6. f=8 7. u=5 8. c=1 9. s=8 10. q=1/7 11. k= 1/5 12. j=9 13. r=120 14. b=1.4 15. g= 3.1 and 16. m=25

Step-by-step explanation:

Which choice is equivalent to the fraction below when x is an appropriate value? Hint: Rationalize the denominator and simplify. 7/7+√14x
A. 7-√14x/7-2x
B.7-√14x/49-14x
C.7-√14x/49-2x
D.7-√14x/7-14x​

Answers

Answer:

A. (7 - √14x) /(7 - 2x)

Step-by-step explanation:

Given the fraction:

7 / (7 + √14x)

Rationalize the denominator by multiplying (7 - √14x):

7 / (7 + √14x) =7(7 - √14x) / (7 + √14x)(7 - √14x) =7(7 - √14x) /(49 - 14x) =7(7 - √14x) /7(7 - 2x) =(7 - √14x) /(7 - 2x)

Matching choice us A

It would be very appreciated mister

Answers

89.95

Steps are on paper.

...what's
[tex] \sqrt{224} [/tex]

Answers

Answer:

it doesnt have any perfect root

Step-by-step explanation:

but in decimal it is 14.97......

Answer:

4√14

Step-by-step explanation:

√224 = √2^5 · 7

         = 4√14

Please help! image below

Answers

Answer:

28 units

hope this helps have an amazing day

Calculate for Area. 5 cm​

Answers

Answer:  25 cm

Step-by-step explanation:

Having trouble solving this:

Answers

Answer:

option b.

61/1000.

................

Answer:

B: 61/1000

Step-by-step explanation:

B: 61/1000 = 0.061

as a percent is 6.1%

Therefore B or 61/1000 is correct hope this helped!

Emily is entering a bicycle race for charity. Her mother pledges $0.20 for every 0.75 miles she bikes. If Emily bikes 15 miles, how much will her mother donate? plz help :D

Answers

Answer:

24 dollars

Step-by-step explanation:

Jackson has scores of 80, 90, 83, and 81 on four Math quizzes. What is the score he needs on the next quiz to achieve an average above 85?​

Answers

He would have to make at least 91.
91. Hope it’s correct.

A circle with radius of 1 cm sits inside a 3 cm x 3 cm rectangle.
Y
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
What is the area of the shaded region?

Answers

Answer:

6.14

Step-by-step explanation:

Find area of shaded region:

regtangle area - circle area = shaded area

Regtangle area:

3x3=9

Circle area:

Pi (3.14) x radius x radius= 3.14

area all together if shaded region

9-3.14=6.14

Find the HCF of 45 and 81.​

Answers

Answer:

3² = 9

Step-by-step explanation:

45 =  3² × 5

81  = 3⁴

================

HCF = 3²

geometry: help me please!

Answers

Answer:

DF = 28 units

AC = 64 units

CF = 32 units

Step-by-step explanation:

In the given triangle ABC points D, E and F are the midpoints of the sides AB, BC and AC.

By midsegment theorem,

"Segment joining the midpoints of each side is parallel and measure the half of the opposite side"

DF = [tex]\frac{1}{2}(BC)[/tex]

     = [tex]\frac{56}{2}[/tex]

     = 28 units

AC = 2(DE)

     = 2 × 32

     = 64 units

CF = [tex]\frac{1}{2}(AC)[/tex]

     = [tex]\frac{64}{2}[/tex]

     = 32 units






If the perimeter of the rectangle shown is 60 feet, we can use the equation 8x + 4 = 60 to find its dimensions. If the solution to this equation is x = 7, what are the dimensions of the rectangle?

Answers

Answer:

l= 28 feet

b = 2 feet

Step-by-step explanation:

The perimeter of a rectangle is given by;

P= 2(l + b)

Comparing this to the equation; 8x + 4 = 60, i can write;

2(4x + 2) = 60

This means that;

l = 4x

b = 2

but x =7

So;

l = 4* 7 = 28 feet

b = 2 feet

Keisha is making potato casserole
for a dinner party. She needs of a
potato per guest. How many
potatoes will she need for 9 guests?​

Answers

Answer:

4 1/2 I think

Step-by-step explanation:

I think but I'm not for sure

Which quotient is reasonable? Do not perform the division. 7315 ÷ 12 A. 6 R 9 B. 60 R 9 C. 609 D. 6,009

Answers

Answer:

C. 609

Step-by-step explanation:

In the question, 4-digits number were given to be divided by a 2-digits number. Without performing the division, it is only reasonable to say that the quotient will be a 3-digits number.

In the given options, the only 3-digits number is 609

Also, you can multiply 609 by 12 to check how reasonable your guess is.

⇒ 609 x 12 = 7308

The difference between 7315 and 7308 is 7.

The remaining number (7) is not up to 12 and when 7 is divided by 12 it will not give a whole number digit.

Therefore, the only reasonable quotient in the given options is 609.

Which expression is equivalent to
(fg) (5)?
F(5)* g(5)
F(5)+g(5)
5f(5)
5g(5)

Answers

Answer:

they F (5) g (5)

Step-by-step explanation:

(fg)=(f.g)

and then this is the first doing (fg)(X)= f(x) [g(x)]

x=5

f(5).g(X)

and they final result is

they top of answer

happy answering

The the composition of f and g denoted by the expression (fg)(5) is equivalent to f(g(5))

What is composition of functions?

The composition of two functions f and g is an operation where two functions f and g generates a new function h such that h(x)=f(g(x)).

First we find the value of g(x). If g(x)=y then f(g(x))=f(y).

The value of composition  (fg)(x) is equal to f(g(x)).

Thus the value of (fg)(5) is f(g(5)) .

If g(5)=c , some c.

Then (fg)(5)=f(g(5))=f(c)

Hence the value of the composition of f and g of 5 is f(g(5)).

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There is an unknown number of people at the table at the
beginning of lunch. Then...
3 more people joined the group.
Then the entire group divided into 2 groups, and
one group left and went outside,
of the total students were left in the lunchroom
5 people joined the group in the lunchroom.
The total number of people in the lunchroom at the
end of lunch was 10

a. Write the equation you can create to show this situation.

b. How many people were at the table at the beginning of lunch? Explain how you know.

Answers

Answer:

11 hours ago u prob dont need it

Step-by-step explanation:

123456

if Seth used 4 ounces of black beans, how many beans did he use altogether?​

Answers

Answer: 4 Ounces.

Step-by-step Explanation: I don't know the full context of the problem, but if Seth used 4 ounces, that means that he used 4 ounces all together.

What is the sum of 3/8 + 2/5

Answers

3/8 + 2/5 = 31/40

the fractions have unlike denominators. first, find the least common denominator and rewrite the fractions with the common denominator. multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. this is basically multiplying each fraction by 1. Once you complete the multiplication and the equation you should have 15/40 + 16/40. Since the denominators are alike all you have to do is add the numerators and you’ll have 31/40. hope I helped

Expand and combine like terms.
(7b^5 – b^2)^2

Answers

i got 49b^10-14b^7+b^4

Marcus believes he can score a goal at least 70% of the time.He runs a simulation where he tracks the number of successful goals out of ten attempts. He runs the simulation 100 times.
Goals 0 1 2 3 4 5 6 7 8 9 10
Frequency 0 1 2 2 1 0 1 18 40 30 5
He decides to use a significance level of 0.05. What can he conclude about his null hypothesis that he will score no more than 6 goals out of 10?

Answers

Answer:

The p-value is 0.07, which is more than 0.05. Fail to reject the null hypothesis.

Step-by-step explanation:

Other Questions
A(n) _____ is created when the parties involved have knowingly and intentionally agreed on the promises and performances. PlastiPharm produces a foundational product that sits on a shelf until it is needed and added to another product. In reviewing the process of combining the two products, the production staff realized that the foundational products are sometimes not tested, although the final product is always tested. They determined that all the foundational products will now undergo testing. The additional testing will add time and effort, which translates to additional costs, so why would PlastiPharm want to perform the additional testing?a.The additional testing helps the company as it strives for perfection in its products and helps avoid future problems by reducing waste (defective parts).b.Making sure that all parts are tested ensures that the company is ready to respond to last-minute orders.c.The additional testing will help the company meet customer demands for certification that all their products have been tested 100 percent of the time.d.Testing all the parts addresses any questions that customers might have about quality or performance of materials. HELP ME PLEASEEEPart ATo begin, either select a topic from previous lessons in this unit orchoose a new topic of interest. Write the topic you have selected.Tip: If you haven't already selected a topic, consider these suggestionsfor choosing a topic. 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The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65 E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80 E from the Pine Knob and S 70 E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)From Pine Knob: Determine the domain and range of the following and show/explain your work.5 y = - x^4 + 4 Provide a graph to verify your answer.6 y = 2x^3 - 1 Provide a graph to verify your answer.7 y = 3(2x+8) Provide a graph to verify your answer. Find the unknown angle60X30 Which characteristics are typically incorporated into the details of a home-rule charter? White moths were found in huge numbers in the english city of birmingham. these moths could be easily camouflaged by the trees because white lichen covered the bark. because of sudden industrial development, the citys trees became covered with soot. how will this change affect the population of the white moth? a. the population will decrease. b. the population will increase. c. there will be no change in their population. d. the population will change their food preferences. Please someone help me with question a) and b). Ive been having so much trouble with these types of questions. The booklet says that the answers are a) 134degrees and b) 14.3km. I just dont get how to get there. Thank you! [tex]x^{2} +x-12[/tex] solve this polynomial by class 9 corse he expression below was formed by combining different gas laws.V is proportional to StartFraction n T over P EndFraction.Which law was used to determine the relationship between the volume and the number of moles in this equation?Boyles lawCharless lawAvogadros lawGay-Lussacs law A cart of mass 0.5 kg sits at rest on a table on which it can roll without friction. It is attached to an unstretched spring. You give the mass a push with a constant force over a distance of 5 cm in the direction that compresses the spring, after which the mass starts undergoing simple harmonic motion with a frequency of 0.5 complete oscillations per second and an amplitude of 15 cm.A) What is the spring constant of the spring?B) How fast was the cart moving at the instant when you finished pushing it?C) What force did you exert on the cart? Suppose Mai places $3500 in an account that pays 19% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.(a) Find the amount in the account at the end of 1 year.S(b) Find the amount in the account at the end of 2 years. Consider the following code segment: if(!somethingIsTrue()) return false; else return true; } Which one of the following statements would be an accurate replacement for this code necesito ayuda con estas operaciones 3x=123x= -5=0x+4=179y+3=215(x-2)=20x2=42x=45x=24x+5=3x-63(x-2) =0x3-4=05(7-x) =31-x3(2x-2) =2(3x+9)