Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation. t2 (dy/dt) + y2 = ty

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]t^2 \dfrac{dy}{dt}+ y^2 = ty \\ \\ t^2 \dfrac{dy}{dt}-ty = -y^2[/tex]

[tex]\text{by dividing both sides by }{y^2},\text{ we have:}[/tex]

[tex]\dfrac{t^2}{y^2}\dfrac{dy}{dt}- \dfrac{ty}{y^2}= -1[/tex]

[tex]\dfrac{t^2}{y^2}\dfrac{dy}{dt}- t\dfrac{1}{y}= -1[/tex]

[tex]\text{by dividing both sides by }t^2; \text{we have;}[/tex]

[tex]\dfrac{1}{y^2}\dfrac{dy}{dt}- \dfrac{1}{t}\dfrac{1}{y}= -\dfrac{1}{t^2}--- (i)[/tex]

[tex]Let \ v = \dfrac{1}{y}[/tex]

[tex]\dfrac{dv}{dt}= -\dfrac{1}{y^2}\dfrac{dy}{dt}[/tex]

[tex]-\dfrac{dv}{dt}= \dfrac{1}{y^2}\dfrac{dy}{dt}[/tex]

[tex]\text{replace in equation (1); we have}[/tex]

[tex]- \dfrac{dv}{dt}-\dfrac{1}{t}v = -\dfrac{1}{t^2}[/tex]

[tex]- \Big ( \dfrac{dv}{dt}+ \dfrac{1}{t}v \Big) = -\dfrac{1}{t^2}[/tex]

[tex]\dfrac{dv}{dt}+\dfrac{1}{t}v = \dfrac{1}{t^2}[/tex]

[tex]\text{relating above with} \dfrac{dv}{dt}+ P(t) v = Q(t) \text{, we have:}[/tex]

[tex]P(t) = \dfrac{1}{t} \ \ \ , \ \ \ \ Q(t) = \dfrac{1}{t^2}[/tex]

[tex]\mu (t) = e^{\int P(t) \ dt }= e ^{\int \dfrac{1}{t} \ dt}= e^{In|t|}= t[/tex]

[tex]v\mu(t) = \int \mu(t) Q(t) dt + C[/tex]

[tex]vt = \int (t) (\dfrac{1}{t^2})dt + C[/tex]

[tex]vt = \int \dfrac{1}{t}dt + C[/tex]

[tex]vt = Int+C[/tex]

[tex]v = \dfrac{In \ t + C}{t}[/tex]

[tex]\text{substitute } v = \dfrac{1}{y}}, we \ get}[/tex]

[tex]\dfrac{1}{y}=\dfrac{In \ t +C}{t}[/tex]

[tex]\mathbf{y = \dfrac{t}{In \ t + C}}[/tex]


Related Questions

Please help me with this ᕕ( ᐛ )ᕗ thank you!

Answers

Answer:

B

Step-by-step explanation:

We can create the equation step-by-step:

Each row of bricks is 6.5cm and the number of row of bricks is r: 6.5r

Total of height of wall: = 259cm

Top row is 1cm shorter: -1cm

Combine all the terms together and we get: 6.5r - 1 = 259

Which means each row of bricks is 6.5cm but minus 1cm from the top to get 259cm the total :D

Treys grandmother has a framed picture with side lengths that are 12 inches. Trey wants to know how much wall space is needed for the picture.

Answers

Answer:

144 inches

Step-by-step explanation:

Answer:

144 inches :)

Step-by-step explanation:

17/2 is bigger than what?​

Answers

Answer:

7/2= 8.5 so it can be bigger then 1/2 or anything under 8.5

Step-by-step explanation:

Determine the missing card value that will result in a product of -324
-6 3 -9

Answers

Answer:

-2

Step-by-step explanation:

-324 ÷ -6 ÷ 3 ÷ -9 = 162

-324 ÷ 162 = -2

A. 2 sqrt 3

B. 4

C. 8

D. 4 sqrt 6

E. 12


Please help

Answers

Answer:

Option B. 4

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 60 °

Opposite (Fe) = 4√3

Adjacent (DE) = x

The value of x can be obtained by using the Tan ratio as illustrated below:

Tan θ = Opposite / Adjacent

Tan 60 = 4√3 / x

√3 = 4√3 / x

Cross multiply

√3 × x = 4√3

Divide both side by √3

x = 4√3 /√3

x = 4

Thus, the length of DE is 4

one bar of candy A and two bars of candy B have 769 calories. Two bars of candy A and one bar of candy B contain 776 calories. Find the caloric content of each candy bar. ​

Answers

Step-by-step explanation:

Hjqjzjzj is a complete* of the following elements has the largest atomic size in the world is the difference between human rights

Answer:

We know:

A+2B=777

2A+B=789

 

Let's rearrange the first equation to solve for A:

A=777-2B

 

Now let's plug 777-2B in for A in the second equation, and solve for B:

2(777-2B)+B=789

1554-4B+B=789

1554-789=3B

765=3B

B=255

 

Now we can substitute 255 in for B in the first rearranged equation, and solve for A:

A=777-2(255)

A=777-510

A=267

So candy bar A has 267 calories, and candy bar B has 255

I Hope it helps

What geometric term describes PQ and RS

Answers

Answer:

perpendicular lines

Step-by-step explanation:

Two lines in a plane are said to be perpendicular if they intersect in such a way that the angles formed between them are right angles. In the adjoining e, lines PQ and RS intersect at 0 such that ∠ROQ = ∠ ROP = ∠POS = ∠QOS = 90°. Therefore, we say that PQ is perpendicular to RS

Find the H.C.E of 108 and 72.​

Answers

Answer:

36 is the HCF of 108 and 72

Answer:

36.

Step-by-step explanation:

HCF of 108 and 72

108 = 2 * 2 * 3 * 3 * 3

72 = 2 * 2 * 2 * 3 * 3

So picking out the common factors we have

HCF = 2 * 2 & 3 * 3

= 4 * 9

= 36.

What’s the answer please help !!!!

Answers

I think the answer is x>-3
The answer is x > -3

A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate Which of the following is an appropriate method for the biologist to use for inference to the population?
A A one-sample t-interval for a population mean
B A one-sample t-interval for a sample mean
C A one-sample 2-interval for a population proportion
D A matched-pairs t-interval for a mean difference
E A two-sample t-interval for a difference between means

Answers

Answer:

A A one-sample t-interval for a population mean

Step-by-step explanation:

The biologist will collect a random sample of dolphins and use the sample weights to create the estimate.

In a confidence interval, we take the data from the sample and want to estimate it for the entire population, so the interval is for a population mean.

The standard deviation will be taken from the sample, which means that the t-interval is used.

We want for one population, so it is a one sample for the population mean, and the correct answer is given by option A.

Question 1
Which set of numbers below can be used to make a triangle?
10, 1,9
4,8,5
1,1,5
O 2, 6, 12

Answers

Answer:

The Ans is 4,8,5

Step-by-step explanation:

As 8 is the base and 4,5 are sides

Hope it helps you

7 19/22-1 8/11 how do you subtract fractions?

Answers

the answer is 6 3/22
i multiplied the numerator and denominator by 2 of the second equation and subtracted like tht.

Take ur time i just need a anwser ;w;

Answers

Answer:20 people

Step-by-step explanation:

2 x 1/2 x 2 1/2 = 2 1/2
Is this correct?

Answers

Answer:

Yes

Step-by-step explanation:

2 x 1/2 = 1

1 x 2 1/2 = 2 1/2

Answer:

Yes

Step-by-step explanation:

2 x 1/2= 1

1 x 2 1/2= 2 1/2

Calcula el área de los rombos.​

Answers

Answer:

xbxbkzkdkdjd

Step-by-step explanation:

bz va yJnzz

a statement for the equation p-6=10​

Answers

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]p - 6 = 10[/tex]

Required

Write a statement for the expression

The statement is:

The cost of a grater is $6 less than the cost of an electric cooker, What is the of the electric cooker?

The above statement when translated to a mathematical expression is:

[tex]p - 6 = 10[/tex]

Where p represents the cost of the cooker

Solving for p.

[tex]p = 10 + 6 = 16[/tex]

13. Jannah purchased flowers to plant in
her garden. She planted 2 flowers in
each of her 5 flower beds plus 8 flowers
around a pond. Write an expression
that shows how many flowers Jannah
planted.

Answers

Answer:

2x5=10+8

Step-by-step explanation:

my answer need to be 20 characters long so I had to write this too

4 x 3/4 is greater than 3/4 , since 4 is greater than 1. True o false

Answers

Answer:

Trueeee I guessss

Step-by-step explanation:

I don't know

The answer is true! It can’t be False because that’s all correct

bonjour,pouvez vous m’aider ;)
a. calculer DC
b.en déduire que ED =1,60 m
c.une fillette mesure 1,10 m

elle passe a 1,40m derrière la camionnette.
Le conducteur peut-il la voir ? expliquer


Données :
(AE) // (BD)
AE = 1,50 m
BD = 1,10 m
EC = 6 cm

Answers

Answer:

je suis super nul en math desolee

it’s MATH who knows how to do this i’m down bad

Answers

Answer/Step-by-step explanation:

1. 7x + 2 = 5x + 22 (alternate interior angles are congruent)

Collect like terms

7x - 5x = -2 + 22

2x = 20

2x/2 = 20/2

x = 10

2. 13x - 6 = 10x + 24 (alternate interior angles are congruent)

Collect like terms

13x - 10x = 6 + 24

3x = 30

3x/3 = 30/3

x = 10

3. (12x + 26)° + 46° = 180° (same side interior angles are supplementary)

12x + 26 + 46 = 180

12x + 72 = 180

12x + 72 - 72 = 180 - 72

12x = 108

12x/12 = 108/12

x = 9

4. (5x + 5)° + 135° = 180° (same side interior angles are supplementary)

5x + 5 + 135 = 180

5x + 140 = 180

5x + 140 - 140 = 180 - 140

5x = 40

5x/5 = 40/5

x = 8

1. A bank account started with $1000 and earned $10 interest per month
for two years. The bank then paid 2% interest on the account for the
next two years.

Answers

Answer:

What exactly is the question here ?? (lol)

In the diagram below, which distance represents the distance from point Qto
RS?

Answers

Answer:

QT

Step-by-step explanation:

Given

The attached diagram

Required

Which distance represents Q to RS

The distance from Q to RS is determined by drawing a perpendicular line from Q to RS.

From the diagram, the perpendicular from Q to RS meets RS at point T.

Hence, the required distance is represented by QT

An economist conducts a nationwide survey to study the financial perceptions of US adults. Specifically, he asks a random sample of 1,000 US adults: “Financially, are you doing OK or are you struggling to get by?” The results of the survey show that 829 of the 1,000 participants said they are doing OK.

(a) Construct a 95% confidence interval for the proportion of US adults who would say they are doing OK.

(b) Shortly thereafter, a similar study is conducted in Mexico with the intention of constructing a 95% confidence interval for the proportion of Mexican adults who would say they are doing OK. What is the smallest sample size that can be used to guarantee that the margin of error will be less than or equal to 0.01?

Answers

Answer:

a) (0.806, 0.852)

b)Margin of error ≤ 0.01

1.96*√{0.5*(1–0.5)/n} ≤ 0.01

√n ≥ 98

n ≥ 9604

• Smallest sample size = 9604

Step-by-step explanation:

I found this on Chegg

Mr. Hernandez dilates the triangle shown below by a scale factor of 2 with the origin
as the center to obtain AA'B'C'.

Answers

Answer: only student 2

Solve for z.
-30 = 5(x+1)

Answers

-30= 5 (x+1 )

-5 from 5= 0
-5 from -30= -35

-35= (x+1)

1/-35= -35

express 75 as prodict of prime factor​

Answers

75 = 1 x 75, 3 x 25,

or

75 = 3 xx 5^(2)

1/2(m - 3) = 1/4(m - 7)
I
Solve

Answers

½m - ³/₂ = ¹/₄m - ⁷/₄

½m - ¹/₄ m = -⁷/₄ + ³/₂

¹/₄ m = -¹/₄

M=-1

Question 5 of 10
Which of the following is most likely the next step in the series?
CO

Answers

C will be the answer as 1st figure have 6 side,2nd figure have 5 side,3rd figure have 4 side then last one will have three side

Answer:

c. because the first one has 6 sides the second one has 5 sides and the third one has 4 sides so that means has 3 sides which is the triangle.

Please refer to the pictures below

Answers

Answer:

D

8-2

Step-by-step explanation:

System of inequalities are

x + y ≥ 7

8x + 7y ≤ 82

can u pls help me i am really stuck this is a geo problem pls get to me as soon as possible thanks.
Question: find the value of x.

Answers

Answer:

Please refer to the attachment

Other Questions
visual art question PLEASEEEEEE HELP ME AND SOON:Imagine you are an Underground Railroad conductor. Create three to five journal entries of three to five sentences each about your interactions with slaves escaping to the North. You may choose which state you live in, where you choose to help, what you provide, what time of year it is, etc. Can you just get KA answers from somewhere Help me? pleases someone actually help i dont get it look at the screenshota,b, or c Which is the median of this set of data?1822 11 21 78 11A 20.5B 21C 18D) 19.5 As atmospheric CO2 increases, the amount of CO2 dissolved in seawater is expected to increase as well. This produces more carbonic acid, which then dissociates into hydrogen ions and something else. sin=24/25, find the cos determine las partes por millon del mercurio, en una muestra que contiene 2500 ml de agua y 0.345 g de mercurio If Danielle can spend no more than $75 on clothes, and wants a pair of shoes for $40 and will spend the rest of the money on $12 scarves, what is her rate of change ? Someone plz help me I will give brainliest Draw a rhombus with diagonals 4 and 6. What is the area of the rhombus? Find the product of 2x4(3x2 + 4x + 1). 6X6 + 8x5 + 2x4 6x3 + 3x4+1 5X6 + 6x5 + 3x4 5x8 + 6x4 + 1 Practice Problem #2: How many atomsof Ba are in 7.8 moles of Ba? t 7.5 hours at the zoo. If he left at 4:20 pm., what time did he arrive at the zoo During electrolysis, where do reduction reactions occur?A. in the anode of an electrolytic cellB. in the cathode of an electrolytic cellC. in the power source of an electrolytic cellD. in the salt bridge of an electrolytic cell Find the Perimeter and Area Resumen de ventajas y desventajas que se obtienen al realizar un control de las mercancas Solve this system of equations.Write your answer as an ordered pair.3x+4y=36 y=-1/2x+8 What do the Selma marches connect to the Civil RIghts movement?