Verify that all members of the family y =(c - x2)-1/2 are solutionsof the differential equation. (b) Find a solution of the initial-value problem. Y=xy^3, y(0)=3 y(x)=????In (b) i have got y = +/- root 1/-x^2+1/9My teacher said to be I must use (a). I do not for what I shoulduse (a). Please solve the problem for me.

Answers

Answer 1

The family of functions y = (c - x^2)^(-1/2) satisfies the given differential equation y = xy^3. By substituting y = (c - x^2)^(-1/2) into the differential equation, we can verify that it holds true for all values of the constant c. For the initial-value problem, y(0) = 3, we can find a specific solution by substituting the initial condition into the family of functions, giving us y = (9 - x^2)^(-1/2).

1. To verify that the family of functions y = (c - x^2)^(-1/2) satisfies the differential equation y = xy^3, we substitute y = (c - x^2)^(-1/2) into the differential equation.

  y = xy^3

  (c - x^2)^(-1/2) = x(c - x^2)^(-3/2)

  Multiplying both sides by (c - x^2)^(3/2), we get:

  1 = x(c - x^2)

  By simplifying the equation, we can see that it holds true for all values of c. Therefore, all members of the family y = (c - x^2)^(-1/2) are solutions to the differential equation.

2. For the initial-value problem y(0) = 3, we substitute x = 0 and y = 3 into the family of functions y = (c - x^2)^(-1/2):

  y = (c - x^2)^(-1/2)

  3 = (c - 0^2)^(-1/2)

  3 = c^(-1/2)

  Taking the reciprocal of both sides, we get:

  1/3 = c^(1/2)

  Therefore, the specific solution for the initial-value problem is y = (9 - x^2)^(-1/2), where c = 1/9. This solution satisfies both the differential equation y = xy^3 and the initial condition y(0) = 3.

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Related Questions

Please help ten points

Answers

A=70 degrees
B=55 degrees
C=25 degrees

A sum amount to $2400 at 15% simple interest per annum after 4 years. Find the sum

Answers

Answer:

1500

Step-by-step explanation:

We can required to find the sum which also means the value

Future value= value × [ 1 + rate×time]

2400= value × [1 + 15/100×4]

2400= value × [1 + 0.15×4]

2400= value × [1+0.6]

2400= value × 1.6

Value= 2400/1.6

= 1500

How do you write 75% as a unreduced fraction

Answers

Answer:75/100

Step-by-step explanation:

75%=75/100

Answer:

75/100

Step-by-step explanation:

reduced fractions of this include but are not limited too: 3/4 6/8 12/16 24/32 48/64

At Garcia's Bike Rentals, it costs $45 to rent a bike for 8 hours. How many hours of bike use does a customer get per dollar?

Answers

Answer:

5

Step-by-step explanation:

Answer:

$0.09/minute

Step-by-step explanation:

$45/8 hours is $5.63 per hour

There is 60 minutes in an hour.

So you do $5.63/60 minutes and it's about $0.09

So it's 9 cents per minute

hope this helps :)

Solve for X: X+8=3(x-7)-5

Answers

Answer:

x = 17

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right  

Distributive Property

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

x + 8 = 3(x - 7) - 5

Step 2: Solve for x

Distribute 3:                                                                                                      x + 8 = 3x - 21 - 5Combine like terms:                                                                                       x + 8 = 3x - 26[Subtraction Property of Equality] Subtract x on both sides:                      8 = 2x - 26[Addition Property of Equality] Add 26 on both sides:                                34 = 2x[Division Property of Equality] Divide 2 on both sides:                                17 = xRewrite/Rearrange:                                                                                        x = 17

Answer:

17

Step-by-step explanation:

X+8=3(x-7)-5

x+8=3x-21-5

x+8=3x-26

8=2x-26

34=2x

(Look at attached imagine)

Answers

Answer:

C.  [tex]r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]

Step-by-step explanation:

At a sale, dresses were sold for $192 each. This price was 96% of the dress's original price. How much did a dress originally cost?​

Answers

Answer:

$199.68

Step-by-step explanation:

You would have to find 4% of 192.

That is 7.68.

192+7.68=199.68.

Are the two expressions in the equation 2b + 5 + 1b = 3b + 5 equal or equivalent? How do you know

Answers

yes , because if you join all like terms , on the side of (2b+5+1b) you would get the equation 3b + 5 .

Which of the following answers would have
no solution?
X=3
5=3
2=2

Answers

Answer:

no entiendo me explican que significa por fa

The answer to the following would be because the others are possible 5=3

what is the sum of 7 and t/2

Answers

Answer:

14/2+t/2 so ( 14+t)/2 is the answer

7+(t/2) =
(7)(2)+(t)(1) /(2) (1)
=(14+t)/(3)

Suppose f(x)=x^2 +1. Find the graph of 4 f(x).
Graph 1
Graph 2

Answers

Answer:

Graph 1.

Step-by-step explanation:

The graph of f(x) will be compressed by a factor 4 and the vertex will be 4 units up from the origin.

HELP MEEEEE PLEASEEE

Answers

Answer:

i do not know but you need to answer you text messages

Step-by-step explanation:

A point P os equi distant from R(-2,4) and S(6,-4) and its x co ordinate is twice its Y co ordinate find co ordinates of P

Answers

Answer: [tex]P(-4,-2)[/tex]

Step-by-step explanation: Distance between two points is calculated as

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

Equidistant means the same distance, i.e., the distance between points P and R is equal to the distance between points P and S.

Suppose P's y-coordinate is a. If its x-coordinate is double, then

(x,y) = (2a,a)

Thus

[tex]\sqrt{(2a+2)^{2}+(a-4)^{2}} =\sqrt{(2a-6)^{2}+(a+4)^{2}}[/tex]

Solving

[tex]4a^{2}+8a+4+a^{2}-8a+16=4a^{2}-24a+36+a^{2}+8a+16[/tex]

[tex]5a^{2}+20=5a^{2}-16a+52[/tex]

[tex]-16a=32[/tex]

[tex]a=-2[/tex]

y-coordinate is [tex]-2[/tex], then x-ccordinate is

2a = 2(-2) = [tex]-4[/tex]

Coordinates of point P equidistant for R and S is [tex](-4,-2)[/tex].

1.) 87.743
2.)123.789
3.) 3256.1254
4.) 102356.78
5.) 78.56
Round to whole number..​

Answers

Answer:

1.)88

2.)124

3.)3256

4.)102357

5.)79

Step-by-step explanation:

A vending machine sells chips for $0.50 and candy bars for $1.00. If Jim spent $5.50 on snacks in the machine over the course of a week, how many candy bars did he buy? G. 2 H. 3 J. 4 K. Cannot be determined from the given information

Answers

Answer:

can't be determined

Step-by-step explanation:

we would need to know the total number of bars/chips he brought

Solve for x
Solve for x

Answers

Answer:

x=19

Step-by-step explanation:

20/36=30/(x+5+30)

20(x+35)=30(36)

20x+700=1080

20x=380

x=19

x is 19 you’re welcome

plz solve it
all the 3 sub questions
chapter quadrilaterals
9 cbse ​

Answers

Answer:

I edited answer

hope it helped

What is the height of the boat in the scale model?
What length is the real boat?

Answers

Answer:

15

Step-by-step explanation:

a) The height of the real boat is 15 feet and the scale model is 3 inches

b) The scale model is 9 inches , and the real height is H = 45 feet

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

The proportion of scale model of the boat to the real boat is 1 : 5

Now ,

a)

The height of the real boat is 15 feet and the scale model is k inches

From the proportion , we get

1 / 5 = k / 15

Multiply by 15 on both sides , we get

k = 3 inches

b)

The scale model is 9 inches , and the real height is H

From the proportion , we get

5 / 1 = H / 9

Multiply by 9 on both sides , we get

H = 45 feet

Hence , the proportion is solved

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JJack, Jill, and Bill each carried a 48-fluid ounce bucket full of water down the hill. By the time they reached the bottom, Jack's bucket was only 3/4 full, Jill's was 2/3 full, and Bill's was 1/6 full. How much water did they spill altogether on their way down the hill?

Answers

Answer:

Jill lost 1/3

Bill lost 1/6

and Jack lost 1/4

Make a common denominator -  let's use 12

Jill lost 4/12

Bill lost 2/12

Jack lost 3/12

Add them together = 9/12

reduce by dividing by 3.

total of 3/4 spilt

48 divided into 4 parts then multiplied by 3 of those parts

48 / 4 * 3 = 36

Step-by-step explanation:

6 + 4y = Y-6

hurry please giving 15 points

Answers

Answer:

y= -4

Step-by-step explanation:

what would be the reminder of 20,000 divided by 24 ?

Answers

Answer:

I think 2500..not sure tho

Step-by-step explanation:

Which table and graph represent the equation y = 3X?
—————————
a.table B and graph A
b.table B and Graph B
c.table A and graph B
d.table A and graph A

Answers

Answer:

d. table A and graph A

Step-by-step explanation:

y=3x

y = 3X is represented by graph B .

y = 3X is represented by table A .

Hence option C is correct .

Given, Equation : y = 3X

Now, to get the values of y substitute x.

Firstly table A:

y = 3X

x = 1 : y = 3

x = 2 : y = 6

x = 3 : y = 9

Thus table A represents the equation .

Next graph B :

Starting point of graph B is origin.

Coordinates of origin : (0,0)

Equation of graph B : y = 3X

Thus graph B represents the equation .

Therefore option C is correct .

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Megan is planning to make dinner for a group of friends. She wants to make each person a personal pizza. It takes Megan 3 minutes to prepare a personal pizza with toppings. The function P(f) = 3f represents the time it takes to prepare the pizzas, where f is the number of friends attending her dinner party.
The function C(f) = 30 represents the time to cook the pizzas since it will take Megan 30 minutes regardless of how many friends attend..
Which expression represents how long it will take Megan to prepare and cook the pizzas

A. P(f) + C(f)
B. P(f) – C(f)
C. P(f) ∙ C(f)

Answers

Answer:

The answer is A

Step-by-step explanation:

You are adding the time it takes to make a pizza so it isn't B or C

The sum of my number and two and two thirds is seven. What is my number?

7 is in one box. Below it are 2 boxes. N is in one. 2 and 2-thirds is in the other.

Check all that apply.
The variable, n, represents the unknown number.
The unknown number and 2Two-thirds equals 7
4One-third+2Two-thirds= 7
9Two-thirds- 2Two-thirds= 7
n = 4One-third

Answers

Answer:

1,2,3,5

Step-by-step explanation:

Answer:

abce

Step-by-step explanation:

Using technology, determine the monthly payment on a 35 month loan of $28,000 at 8.1% compounded monthly. Round your answer to the nearest cent.
Please select the best answer from the choices provided
A. $900.90
B. $875.02
C. $1,102.94
D. $1,012.10

Answers

Answer: a

Step-by-step explanation:

Took test

Write a story to match the equation: x + 2 1/2 = 10
Lin likes to bake batches of muffins and share them with friends and family. She needs 10 cups of flour for her next batch, but only has 2 1/2 cups left. How much more flour does she need?

Answers

Answer:

She needs 15/2 cups of flour.

Step-by-step explanation:

x+2 1/2=10

2 1/2=5/2

x+5/2=10

x=10-5/2

x=20/2-5/2=15/2

Jennifer has 12 nickels and dimes. The value of her coins is $1

Answers

Answer:

4 dimes, 12 nickels

Step-by-step explanation:

nickels are worth 5 cents,

12x5=60

$1 is worth 100 cents

100-60 is 40

dimes are worth 10 cents

40 / 10 is 4

so 4 dimes

The number of dimes = 8 dimes

The number of nickels = 4 nickels

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of nickels be = x

Let the number of dimes be = y

Now , the total number of coins = 12

So , the equation will be

x + y = 12   be equation (1)

Now , the total value of coins = $ 1

The value of 1 dime = $ 0.10

The value of 1 nickel = $ 0.05

So , the equation will be 0.05x + 0.10y = 1   be equation (2)

Multiply equation (2) by 100 , we get

5x + 10y = 100   be equation (3)

Multiply equation (1) by 5 , we get

5x + 5y = 60   be equation (4)

Subtracting equation (4) from equation (3) , we get

5y = 40

Divide by 5 on both sides of the equation , we get

y = 8

Therefore , the value of y = 8

Substitute the value of y in equation (1) , we get

x + y = 12

x + 8 = 12

Subtracting 8 on both sides of the equation , we get

x = 4

Therefore , the value of x is 4 and value of y is 8

Hence , The number of dimes = 8 dimes

The number of nickels = 4 nickels

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Helppppppp meeeeeee pleaseeeeee asappp

Answers

Answer:

C

Step-by-step explanation:

open circle, arrow pointing left

C will be your answer

Select all the statements that are true about rhombuses. Group of answer choices
Opposite angles are congruent.

Diagonals are congruent.

Diagonals bisect each angle.

Diagonals are perpendicular.

Opposite sides are parallel.

Answers

Step-by-step explanation:

By method of elimination;

- Opposite angles are congruent

Congruent means Equal

This is correct.

- Diagonals are congruent

This is incorrect.

- Diagonals bisect each angle.

This is correct.

- Diagonals are perpendicular.

This is correct.

- Opposite sides are parallel.

This is correct.

Answer:

- Opposite angles are congruent

- Diagonals bisect each angle.

- Diagonals are perpendicular.

- Opposite sides are parallel

The blizzard company sent a survey to their world of warcraft subscribers and asked if they were expected about the up coming expansion. From the survey, 16 people of the 20 people surveyed said they were excited. A) the probability that 2 people were excited without replacement is

Answers

Answer:

0.6316

Step-by-step explanation:

The computation of the probability that 2 people were excited without replacement is shown below:

There is a total of 20 people

out of which 16 are excited and the remaining 4 would be non-excited

Now the probability would be

[tex]= \frac{^{16}C_2}{^{20}C_2}[/tex]

= 0.6316

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What are the lengths of the legs of a right triangle in which one acute angle measures 19 and the hypotenuse is 15 units long? Round answers to the nearest tenth. 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