Find the general solution to the differential equation (1+x)dy-2ydx=0

Answers

Answer 1

Tthe general solution to the differential equation is given by y = (1+x)^2C, where C is any real number.

The given differential equation is (1+x)dy - 2ydx = 0. To find the general solution, we can rearrange the equation as dy/dx = 2y/(1+x) and separate the variables, yielding (1/y)dy = (2/(1+x))dx. Integrating both sides gives us ln|y| = 2ln|1+x| + C, where C is the constant of integration. Simplifying further, we get ln|y| = ln|(1+x)^2| + C, which can be rewritten as ln|y| = ln|((1+x)^2e^C)|. By taking the exponential of both sides, we obtain y = (1+x)^2e^C, where C is an arbitrary constant.

In this differential equation, we initially rearrange it and separate the variables to obtain dy/dx = 2y/(1+x). Then, we integrate both sides, resulting in ln|y| = 2ln|1+x| + C. We simplify further by exponentiating both sides, which leads to y = (1+x)^2e^C. The constant of integration, C, is absorbed into a new constant, let's say C' = e^C. Therefore, the general solution to the differential equation is y = (1+x)^2C', where C' represents any real number.

This solution represents a family of curves that satisfy the original differential equation, and different values of C' will give different curves within this family.

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Related Questions

Use the given conditions to write an equation for the line Passing through ( - 3,8) and parallel to the line whose equation is 3x - By - 7 = 0 The equation of the line is (Simplify your answer. Type an equation using x and y as the variables.

Answers

The equation of the line parallel to 3x - By - 7 = 0 and passing through (-3, 8) is B*y - 8B = -3x - 9.

To find the equation of a line parallel to the given line, we need to determine the slope of the given line. The equation of the given line is 3x - By - 7 = 0.

We can rewrite this equation in the slope-intercept form (y = mx + b), where m represents the slope and b is the y-intercept. By rearranging the equation, we have:

By - 7 = -3x

By = -3x + 7

Dividing both sides by B (assuming B ≠ 0):

y = (-3/B)x + 7/B

From the equation y = (-3/B)x + 7/B, we can see that the slope of the given line is -3/B.

Since the line we're looking for is parallel to the given line, it will have the same slope. Therefore, the slope of the line we seek is also -3/B.

We are given that the line passes through the point (-3, 8). We can use the point-slope form of a line to find the equation:

y - y1 = m(x - x1)

Substituting the values (-3, 8) for (x1, y1) and -3/B for m:

y - 8 = (-3/B)(x - (-3))

y - 8 = (-3/B)(x + 3)

Multiplying through by B:

By - 8B = -3(x + 3)

Simplifying:

B*y - 8B = -3x - 9

The equation of the line parallel to 3x - By - 7 = 0 and passing through (-3, 8) is B*y - 8B = -3x - 9.

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Hello, can someone please assist me with this problem.

Answers

So for this problem you need to find the length of a side of the square. To do this you can use Pythagorean theorem to find the length of the right triangle with the side of the square as it’s hypotenuse.
The Pythagorean theorem is:
a^2 + b^2 = c^2
a = 1 and b = 3
1^2 + 3^2 = c^2
10 = c^2
square root of 10 = c

Now that we know the length of the side, we can find the area of the square. Area of a square = side^2, so:
Area = (square root of 10)^2 = 10

The area of the square is 10!

Pleaseee answer these two questions helppppp ill give you brainliest answer if you knowwww help pleaseeee

Answers

Answer:

The theoretical probabilty of the coin landing on tails is 50/50 so their is a 50% chance of it landing on tails so theoretically it would land on tails 15 out of 30 times

Step-by-step explanation:

what is the diameter of a circle with a circumference of 56 inches?

Answers

Answer:

17.83in

Step-by-step explanation:

Diameter of circle with circumference 56 inches 17.81 inches .

Given,

Circumference = 56 inches

Now,

Circumference of circle = 2πr

r = radius of circle.

Substitute the values to get the value of radius,

56 = 2 × π × r

56 = 2× 22/7× r

r = 56 × 7/44

r = 8.909 inches.

Next,

Diameter = 2 (Radius)

Diameter = 2 * 8.909

Diameter = 17.81 inches .

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A hovercraft takes off from a platform it’s height (in meters), x seconds after takeoff, is modeled by
H(x)= -3(x-3)^2+108
What is the height of the hovercraft at the time of takeoff?
PLS I NEED THIS ASAP

Answers

9514 1404 393

Answer:

  81 m

Step-by-step explanation:

Since x is seconds after takeoff, the value of x at takeoff is 0. You are being asked to find H(0).

  H(0) = -3(0 -3)^2 +108 = -3(9) +108 = 81

The height of the hovercraft at the time of takeoff is 81 meters.

Pls help me I don't get it.
Pls indicate steps

Answers

I'm having trouble reading, could you type out what is on the picture? I'll edit my answer then.

Answer:

x = -3, y = 3

Step-by-step explanation:

multiply the equation 3y - x = 12 by 3:

=> 9y - 3x = 36

now add the two equation 9y - 3x = 36 and 3x + 4y = 3 together to eliminate x and solve for y:

=>    9y - 3x = 36

 +)   4y + 3x = 3

______________

       13y        = 39

=>       y         = 3

substitute y = 3 into the original equation 3y - x = 12 to solve for x:

3(3) - x = 12

=> -x = 12 - 9

=> -x = 3

=> x = -3

You will get 40 points if you help me and Brainliest!

Answers

Answer:

The answer is c It is hard to explain so sorry

Answer:

C

Step-by-step explanation:

The bus spans from 10 to 20 the absolute value of that is 10 the teachers span from 15 to 30 the absolute value of that is 15 making the teachers 5 miles more than the buses.

In one year, a principal of $1000 led to an accumulation of $1100 .

The annual percentage yield ( APY ) for this investment is 9 % .

True

False

Answers

In one year, a principal of $1000 led to an accumulation of $1100. The annual percentage yield ( APY ) for this investment is 9 %. False.

The annual percentage yield (APY) is not 9% in this case. The APY takes into account the compounding of interest over the course of a year and provides a more accurate representation of the actual return on the investment. In this scenario, the investment of $1000 growing to $1100 in one year represents a simple interest rate of 10%. The APY would be higher than 10% if the interest was compounded.

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anyone know the answers to 3, 4, 5 and six

Answers

3) would be D ! , 4) would be letter J , & 5) would be letter C ! Hope it helps !!!

Find m∠MON..........

Answers

MON = 15°

LOM + MON = LON in measure, so
9x + 44 + 6x + 3 = 77
15x + 47 = 77
15x = 30
x = 2

MON = 6x + 3
= 6(2) + 3
= 12 + 3 = 15°

Lin understands that expanding is using the distributive property, but she doesn’t understand what factoring is or why it works. How can Kiran explain factoring to Lin?

Answers

Kiran can explain factoring to lin by finding what multiples together to get an expression. It is in a way, like splitting an expression into multiplication easier expressions.

Answer:

doing this so other guy gets brainliest

Step-by-step explanation:

Hey I know this is kind of a lot but can someone pls help.

Answers

Answer:

J) x = 6; slope is undefined

Step-by-step explanation:

Choice F is incorrect because the equation and slope. Choice G is incorrect because the slope. And, Choice H is incorrect because the equation and the slope.

Write the equation of a line in slope intercept form that passes through (3,-2) and (0,-5)

Answers

Answer:

y=x-5

Step-by-step explanation:

First, you find the slope by -2-(-5)/3-0. This would be 3/3 which is equal to 1. Then you plug in the x with any point you want. I'm going to use (3,-2). The equation should look like -2=3+y. Now we find what is y. Therefore for this equation to be true. Y is equal to -5. Now put it all together. Y=x-5. You can use the other point to check my answer!  Hope that helps!!

In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If 10000 students participated in the poll, how many chose Orange?

Answers

Answer:

2100

Step-by-step explanation:

10,000 x 21%

10000 x 0.21 = 2100

CAN SOMEONE PLEASE HELP ME

Answers

TSR because if u look at the lines of where their similar on the second one you match it up

(450) + (28.75x) = 967.50
solve for x

Answers

Answer:

18

Step-by-step explanation:

Hello,

In order to solve for x, we need to isolate the variable on one side of the equation.

To do this, we subtract 450 from both sides of the equation, and this will give you:

28.75x = 517.5

As mentioned, we need to isolate x, so we divide both sides by 28.75. This will give the following.

x = 18

Hope this helps!

What is the monthly payment for an $8,720 loan at 12.5 percent for 15 years?
$107.43
$10,617.40
$16,088.40
$19,337.40​

Answers

The monthly payment for an $8,720 loan at 12.5 percent for 15 years is $312.84

How to calculate the compound interest

The formula for calculating the compound interest is expressed as:

A = P(1+r/n)^nt

Given

P = $8720

r = 12.5% = 0.125
n = 12
t = 15

Substitute

A = 8720(1+0.125/12)^180
A = 1.8622 *  8720

A = $56,312.74

Monthly payment = 56,312.74/180
Monthly payment = 312.84

Hence the monthly payment for an $8,720 loan at 12.5 percent for 15 years is $312.84

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I really need help please and thank you

Answers

Answer:

x = 8

Step-by-step explanation:

You can set up the equation 6/4 = 12/x and then cross multiply to solve for x

If a pack of highlighter costs 2.40 what is the cost Per highlighter, in dollars and cent

Answers

From the information you gave me, I am going to guess it is a 4 pack of highlighters.

Answer: $0.60 per highlighter

Explanation: To find the unit rate of an item, take the price ($2.40) and divide it by the amount of the product included (4).

Find the value of x, then find each angle measure.

Answers

Answer:

x = 9

m<J = 57

m<K = 44

m<L = 79

Step-by-step explanation:

Theorem:

The sum of the measures of the angles of a triangle is 180°.

We add the measures of the angles, and set the sum equal to 180. Then we solve for x, and use the value of x to find the measure of each angle.

7x - 6 + 3x + 17 + 9x - 2 = 180

Combine like terms on the left side: 7x + 3x + 9x = 19x and -6 + 17 - 2 = 9

19x + 9 = 180

Subtract 9 from both sides.

19x = 171

Divide both sides by 19.

x = 9

Now we find the measure of each angle.

m<J = 7x - 6 = 7(9) - 6 = 63 - 6 = 57

m<K = 2x + 17 = 3(9) + 17 = 27 + 17 = 44

m<L = 9x - 2 = 9(9) - 2 = 81 - 2 = 79

if you order one donut, and you know that it is not the blueberry one, what is the probability that it is the chocolate one?

Answers

Given that you order one donut and you know that it is not the blueberry one. We need to determine the probability that it is the chocolate one.

Say we have 3 flavors of donuts such as Blueberry, Chocolate and Glazed. There are a total of 3 possibilities for the first choice. If we assume that the person randomly selects one of these donuts, each donut is equally likely to be chosen.

Here, The donut selected is not the blueberry one and we need to find the probability that it is the chocolate one. Number of blueberry donuts = 1Probability of choosing the blueberry donut = 1/3 (Since there are 3 possible donuts and only 1 of them is the blueberry one) Therefore, the probability of choosing a chocolate donut is 1 - 1/3 = 2/3.

Similarly, the probability of choosing a glazed donut is also 2/3. Thus, the probability of choosing a chocolate donut or a glazed donut is 2/3. Answer: 2/3.

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carol is making baby blankets for her daughters twins. If one blanket needs 43/4 yd of fabric, how much fabric does carol need for two blankets?

Answers

Answer:

21 1/2 yd

Step-by-step explanation:

43/4 + 43/4 = 21 1/2 yd

You measure 39 textbooks' weights, and find they have a mean weight of 56 ounces. Assume the population standard deviation is 9 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.
Give your answers as decimals, to two places

_____ < μ < _______

Answers

The 95% confidence interval for the true population mean is 53.18 < μ < 58.82

What is the 95% confidence interval?

To construct a 95% confidence interval for the true population mean textbook weight, we can use the formula:

CI = x ± Z * (σ/√n)

where:

x is the sample mean,

Z is the critical value for the desired confidence level (95% confidence corresponds to Z = 1.96),

σ is the population standard deviation, and

n is the sample size.

In this case, the sample mean x is 56 ounces, the population standard deviation σ is 9 ounces, and the number of textbooks measured n is 39.

Plugging these values into the formula, we have:

CI = 56 ± 1.96 * (9/√39)

Calculating the values:

CI = 56 ± 1.96 * (9/√39)

CI = 56 ± 1.96 * (9/6.24)

CI = 56 ± 1.96 * 1.44

CI = 56 ± 2.82

Therefore, the 95% confidence interval for the true population mean textbook weight is approximately:

53.18 < μ < 58.82

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Can someone please tell me the answers

Answers

Answer:

3. [tex]190yd^{2}[/tex] 4. [tex]45cm^{2}[/tex]

Step-by-step explanation:

Area of trapezoid = half the sum of the parallel sides/ bases x the perpendicular height

3. Area of trapezoid = [tex]\frac{(b_{1} +b_{2} )h}{2}[/tex]  

                                 = [tex]\frac{(17+21)10}{2}[/tex]

                                 =  [tex]\frac{380}{2}[/tex]

                                 = [tex]190yd^{2}[/tex]

4. Area of trapezoid = [tex]\frac{(b_{1} +b_{2} )h}{2}[/tex]

                                  = [tex]\frac{(4.5+5.5 )9}{2}[/tex]

                                  = [tex]\frac{90}{2}[/tex]

                                  = [tex]45cm^{2}[/tex]

hope this helps :)

A horse 64 feet from the center of a merry-go-round makes 27 revolutions. In order to travel the same distance, how many revolutions would a horse 16 feet from the center have to make?

Answers

The answer will be 107

. Find the area under the standard normal curve. from z = 0 to z = 1.46 from z = -0.32 to z = 0.98 from z = 0.07 to z = 2.51 to the right of z = 2.13 to the left of z = 1.04|

Answers

The areas under the standard normal curve are:

From z = 0 to z = 1.46: approximately 0.4306From z = -0.32 to z = 0.98: approximately 0.6126From z = 0.07 to z = 2.51: approximately 0.4959To the right of z = 2.13: approximately 0.0161To the left of z = 1.04: approximately 0.8508

What is the area under the standard normal curve?

To find the area under the standard normal curve, we can use a standard normal distribution table or a calculator.

Area from z = 0 to z = 1.46:

Using a calculator, the area under the curve from z = 0 to z = 1.46 is 0.4306.

Area from z = -0.32 to z = 0.98:

Using a calculator, the area under the curve from z = -0.32 to z = 0.98 is 0.6126.

Area from z = 0.07 to z = 2.51:

Using a calculator, the area under the curve from z = 0.07 to z = 2.51 is 0.4959.

Area to the right of z = 2.13:

Using a calculator, the area to the right of z = 2.13 is 0.0161.

Area to the left of z = 1.04:

Using a calculator, the area to the left of z = 1.04 is 0.8508.

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Please help me!!! I will try to mark brainliest if the answer is correct!

Answers

Answer:

I think the first is answer bcz 35+55=90 ..... 180-90=90

heLp pls sOmeBoDy and tyy

Answers

Answer :

AB = 48.88

Step-by-step explanation:

We will use the sin fulmera

[tex] \frac{ \sin(134°) }{ab} = \frac{ \sin(18°) }{21} \\ \\ ab = 48.88[/tex]

I hope that is useful for you :)

Answer:

48.9

Step-by-step explanation:

[tex]\frac{A}{sinA}=\frac{B}{sinB} =\frac{C}{sinC}[/tex]   (you can flip the equation around)

[tex]\frac{21}{sin18} = \frac{AB}{sin134}[/tex]

[tex]AB=\frac{21*134}{sin18}= 48.88448235[/tex]

Sorry for the late answer I was distracted


what are the next three terms of the following sequence
1,4,6,11,21,38

Answers

The next three terms of the sequence 1, 4, 6, 11, 21, 38 are 70, 123, 216.

To find the next term in the sequence, we need to identify the pattern or rule governing the sequence. Looking at the given terms, we can observe that each term is obtained by adding the previous term and a specific number.

From the given sequence:

4 = 1 + 3

6 = 4 + 2

11 = 6 + 5

21 = 11 + 10

38 = 21 + 17

The difference between the consecutive terms appears to be increasing by 1 each time. So, we can infer that the next difference would be 17 + 1 = 18.

Now, to find the next term:

38 + 18 = 56

56 + 19 = 75

75 + 20 = 95

Therefore, the next three terms of the sequence are 70, 123, 216.

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2x + y = 2

x – 2y = -4

what is x and y?

Answers

Answer:

x = 0

y = 2

Step-by-step explanation:

2x + y = 2 (Multiply by 2)

x – 2y = -4

4x + 2y = 4

x – 2y = -4

5x = 0

x = 0

2x + y = 2

2(0) + y = 2

0 + y = 2

y = 2

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