solve the given initial-value problem. x dy dx y = 2x 1, y(1) = 9

Answers

Answer 1

The given initial-value problem is x(dy/dx)y = 2x + 1, y(1) = 9.

To solve this problem, we first rearrange the equation as (1/y) dy = (2/x + 1/x) dx. We can integrate both sides, which gives us ln|y| = 2ln|x| + ln|x| + b, where b is the constant of integration.

Simplifying this expression, we get ln|y| = 3ln|x| + b. Exponentiating both sides, we obtain |y| = eᵇ * x³. Since y(1) = 9, we substitute x = 1 and y = 9 into the equation, which gives us 9 = eᵇ * 1³, or b = ln 9. Therefore, the solution to the initial-value problem is y = ±9x³.

To solve this initial-value problem, we first rearranged the given equation to put it in a form that we can integrate. We then integrated both sides of the equation, introducing a constant of integration. By substituting the initial value of y, we were able to determine the value of the constant of integration and thus find the final solution to the initial-value problem.

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Related Questions

The graph below is the graph of a function.

True or False??

Answers

Answer:

mmmmmmmm I wanna say it's false. like almost positive

Answer true
Explanation: what makes a graph function is a set of points in the plane is the graph of a function if and only if no vertical line intersects the graph in more than one point

Solve for z.
2
39z+ 17z = 0

Answers

Answer:

Z = 0

Step-by-step explanation:

Z is 0 because there’s no other possible solutions

Which inequality is equivalent to -m ≥ 15?

A. m ≥ 15
B. m ≥ -15
C. m ≤ -15
D. m ≤ 15

Answers

Answer:

b I think

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

To solve this equation, since m is negative you need to get rid of that negative by dividing each side by -1. this will leave m and make 15, -15. so the equation will be c, m is less than or equal to -15.


The resale value of a certain car when purchased new is $20,000. The car is expected to lose 10% of its value each year.
Which graph shows the predicted value of the car over time?
HELPPPP I’M GIVING 18 points ASAP




The graph that shows the predicted value of the car over time is the
a. Red graph, 1
b. Blue graph, g
c. Green graph, h
d. Orange graph, k

This makes sense because it’s y-intercept is at
a. 10,000
b. 20,000

And it
a. Increases
b. Decreases

Answers

Answer:

The red graph. y intercept is at 20k and is decreasing

Find the value of each trigonometric ratio. Write your answer as a fraction in simplest form. (Example: If the answer is one-half, type 1/2.)

Answers

The value of each Trigonometric ratio in a right angle triangle given are;  sin X = 4/5 and cos C = 40/41

How to express Trigonometric Ratios?

From the attached image, we can see the triangles to find the trigonometric ratios.

Now, the formula for sin and cos in a right angle triangle is;

sin = opposite/hypotenuse

cos = adjacent/hypotenuse.

Thus;

1) sin X = 32/40 = 4/5

2) cos C = 40/41

Read more about Trigonometric Ratios at; https://brainly.com/question/13276558

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PLS HEL P ASAP NOT THAT HARD!! CONVERT TO ENTIRE RADICAL FORM

Answers

ven a chuparme el huevo

I NEED HELP WITH THIS ASAP!!!!

Lillian is in the business of manufacturing phones.
She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor.

Let CC represent the total cost, in dollars, of producing pp phones in a given day.

The table below has select values showing the linear relationship between pp and C.C.

Determine the fixed cost for rent and equipment.

P C
2 1200
4 1600
6 2000

Answers

Answer:

it's 4,1600

Step-by-step explanation:

I hope my answer can help you

Juan cuts a piece of rope that is 16 meter long into 2 equal pieces.

What is the length of each shorter piece of rope?

Enter your answer as a fraction in simplest form by filling in the boxes

Answers

the length of each shorter piece is 8m long. In a fraction 8/16 which is 1/2.

Theo wants to use a cookie recipe
that makes 36 cookies, but he wants
to increase the number of cookies to
54. If the recipe calls for 2 cups
of sugar, how much sugar should
he use?

Answers

Answer:

1

1

3

cups

Explanation:

This is a ratio question. If we are comparing the ratios, we could say

24

36

=

x

2

where x = the amount of sugar to make 24 cookies.

We can multiply both sides by 2 to cancel the 2 on the right, making

24

(

2

)

36

=

x

.

Simplify this and we get

48

36

and eventually

4

3

or

1

1

3

.

Step-by-step explanation:

You want to do 36/2 then figure out how many time that number goes into 54 and then that’s your answer for how many cups of sugar he should use.

Hope that helps!!

The answer is 3

need help with one question

Answers

Answer:

I think it's x=-4

Step-by-step explanation:

3x= -12

x= -4

The sum of two numbers is 15. Four times the smaller number is 60 less than twice the larger number. What is the larger number?

Answers

Answer:

just put the words into math:

x+y=15

4x = 2y-60

Now just solve the system for y.

i need help urgently lease :D

Answers

Answer:

y=4

-2y=8

y=8/2

xndnndndnd

I need help with this question

Answers

Answer:

R=34

Step-by-step explanation:

As, pythoreon therom states = a2 + b2= c2

a= 16, 16^2 = 256

b= 30, 30^2 = 900

c2= 900+256

c2 = 1,156

c= 34

So, 16^2 + 30^2 = 34^2

Jake needs more than 1 3/5 cups of flour to make cupcakes. Which is greater than 1 3/5? A) 8/5 B) 1 3/4 C) 1 2/5 D 1 3/8

Answers

Answer:

C)  1 3/4

Step-by-step explanation:

A) 1 3/5=1 12/20

B) 8/5=32/20=1 12/20

C) 1 3/4=1 15/20

D) 1 3/8=less than 1 3/4

Answer:  Choice B) 1 & 3/4

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

Work Shown:

Convert each fraction or mixed number into its equivalent decimal form. Use a calculator or long division.

1 & 3/5 = 1 + 3/5 = 1+0.6 = 1.68/5 = 1.61 & 3/4 = 1 + 3/4 = 1 + 0.75 = 1.751 & 3/8 = 1 + 3/8 = 1 + 0.375 = 1.375

The decimal value 1.75 is larger than 1.6, so this shows that 1 & 3/4 is larger than 1 & 3/5

Find the measure of this angle in the triangle.

Answers

Answer:

the angle measures 85 degrees

Three people attend a concert for $155. Ten attend the same concert for $470. Find the rate of change.

Answers

Answer: 45

Step-by-step explanation:

3 attend for $155    ($51.67 a piece)

10 attend for $470 ($47 a piece)

7 more attend/ adds $315

45 is the rate of change

HELPPPPPP
Keisha is working to complete her summer reading in one week so she can relax for the remainder of the summer. She read (2x2 + 5x – 3) pages on Monday, (5x – 3) pages on Tuesday, and (6x2+ 2) pages on Wednesday. How many pages did she read in three days?

Answers

Answer:

(8x² + 10x -4) pages

Step-by-step explanation:

2x² + 5x – 3 + 5x – 3 + 6x²+ 2

2x² +6x² +5x +5x -3-3+2

8x² + 10x -4

A program was created to randomly choose customers at a shoe store to receive a discount. The program claims 15% of the receipts will get a discount in the long run. The manager of the shoe store is skeptical and believes the program's calculations are incorrect. She selects a random sample and finds that 12% received the discount. The confidence interval is 0.12 ± 0.05 with all conditions for inference met.


Part A: Using the given confidence interval, is it statistically evident that the program is not working? Explain.


Part B: Is it statistically evident from the confidence interval that the program creates the discount with a 0.15 probability? Explain.


Part C: Another random sample of receipts is taken. This sample is six times the size of the original. Twelve percent of the receipts in the second sample received the discount. What is the value of margin of error based on the second sample with the same confidence level as the original interval?


Part D: Using the margin of error from the second sample in part C, is the program working as planned? Explain.

Answers

Answer:

A: There is no statistical evidence that the program is not working as intended because 0.15 is between the range of 0.12 ± 0.05 = (0.07,0.17)

B: 0.15 is between the range of (0.07,0.17) so it is statistically probable.

C: margin of error=0.05/((6)^(1/2))=0.0204

D: No the program is not working as planned because 0.15 is not within the range of 0.12±0.0204=(0.0996,0.1404)

Step-by-step explanation:

Within the answer. please tell me if I am wrong

4. Gabby makes banana bread at her bakery every Monday and Wednesday. Her
banana bread calls for the ratio of ingredients shown
5 cups of sugar for every 50 tablespoons of butter
80 tablespoons of butter for every 32 bananas

Answers

Answer:

Top row: 3 cups, 30 tablespoons, 12 bananas

Second row: 7 cups, 70 tbs, 28 bananas

Step-by-step explanation:

The ratio is 5 (sugar) : 50 (butter)...

You can make the unit rate: 1 cup of sugar: 10 tbs of butter

Since the other ratio is 80 tbs : 32 bananas...

1 tbs : .4 bananas

So...

3 cups : 30 tbs

30 tbs : 12 bananas

28 bananas : 70 tbs

70 tbs :  7 cups

Hope this helps!!!

Which of the following angles is corresponding with <5
2
7
8
4​

Answers

Answer:

<7

Step-by-step explanation:

<5 and <7 are cut by the same transversal, so that should be the answer!

Hope that helps!

the question is in the picture. it’s math.

Answers

Answer:

Step-by-step explanation:

1). (8x - 49)° = (5x + 23)°

8x - 49 = 5x + 23

3x = 72

x = 24

2). m∠VST + m∠SVU = 180°

(5(24) + 23)° + m∠SVU = 180°

m∠SVU = 180° - 143°

m∠SVU = 37°

m∠SVT = 37° - 20° = 17°

1. The surface area of a cube whose edges have lengths of 5 inches each is equal to which of the
following?
(1) 25 square inches
(2) 75 square inches
(3) 125 square inches
(4) 150 square inches
5 in
5 in
5 in

Answers

Answer:

150 square inches

Step-by-step explanation:

TSA=6a^2

6*5*5

is 150 square inches

Ashley practiced the piano for 41 minutes. She practiced 13 minutes less than(means subtraction) her brother did. Write and solve an equation to determine how long her brother practiced the piano.(identify the question)

Answers

Answer:

b-13=41

Step-by-step explanation:

Let b stand for the total number of minutes he practiced for. Subtracting 13 from it gets us Ashley's 41, so the equation can be b-13=41.

Four times a number is greater than 48

Answers

Answer:

12

Step-by-step explanation:

Answer:

4x>48

x>12ans.this is the correct answer

Find the slope of the line that passes through (1, 1) and (-3, -5)

Answers

Answer:

3/2

Step-by-step explanation:

(1,1) and (-3,-5)

[tex]\frac{-5-1}{-3-1}[/tex]

Above is the difference of teh y values divided by the difference of x values

we get -6/-4    which is 3/2

PLEASE HELP Find the product of( -3-2i ) and it’s conjugate.

Answers

I believe the answer is -(-3-2i)

If flx) = 2x – 6 and g(x) = x-2x?, find each value.

Answers

Answer:

The question is not correct. you have two linear functions. do you want to know their intersection point?

Step-by-step explanation:

[tex]f(x)=2x-6\\[/tex]

[tex]2x-6=0[/tex]

[tex]2x=6[/tex]

[tex]\frac{2x}{2} =\frac{6}{2\\}[/tex]

x=3

Then you just plug into g(x)

[tex]g(x)=x-2x[/tex]

[tex]g(x)=3-2(3)\\[/tex]

[tex]g(x)= 3-6[/tex]

So,

f(x)=3

g(x)=-3

Karl wants to rent a bike for at most $55. He can rent a bike for $7 per hour plus a $9.50 flat fee. Any portion of an hour is charged as a full hour. What is the maximum number of hours Karl can rent the bike?

Answers

6.5 because you instantly take $9.50 away from $55. After you get that answer, you will have 45.5. Then divide 45.5 by 7 which will give you 6 and a half hours.

Please help me !!!!!

Answers

Answer:

just don't answer that

Step-by-step explanation:

cause I don't know what is the answer

Ok I figured it out I think you just find the letter and then find the reflection I didn’t do them all

Find the area of the figure.
(Sides meet at right angles.)
6 cm
2 cm
2 cm
2 cm
2 cm
2 cm
2 cm
2 cm

Answers

Answer:

paso a paso

Step-by-step explanation:

tienes que saber cuanto bale o la equivalencia de cm 10 haci que

tienes que multiplicar 5 x10 igual con los de mas si te sirvio apoyame plsssss

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