dy/dx=2xy/x²+y² solve​

Answers

Answer 1

Answer:

[tex]y=\frac{-1}{2} \sqrt[]{4x^2+4c_{1}^2} -c_{1}\ or \ \frac{1}{2} \sqrt[]{4x^2+4c_{1}^2} -c_{1}[/tex]

Step-by-step explanation:

As it is first order nonlinear ordinary differential equation

Let y(x) = x v(x)

2xy/(x²+y²)=2v/(v^2+1)

dy=xdv+vdx

dy/dx=d(dv/dx)+v

x(dv/dx)+v=(2v)/(v^2+1)

dv/dx=[(2v)/(v^2+1)-v]/x

[tex]\frac{dv}{dx}=\frac{-(v^2-1)v}{x(v^2+1)}[/tex]

[tex]\frac{v^2+1}{(v^2-1)v}dv=\frac{-1}{x}dx[/tex]

∫[tex]\frac{v^2+1}{(v^2-1)v}dv[/tex] = ∫[tex]\frac{-1}{x}dx[/tex]

u=v^2

du=2vdv

Left hand side:

∫[tex]\frac{v^2+1}{v(v^2-1)}dv[/tex]

=∫[tex]\frac{u+1}{2u(u-1)}du[/tex]

=[tex]\frac{1}{2}[/tex]∫[tex](\frac{2}{u-1} -\frac{1}{u} )du[/tex]

=[tex]ln(u-1)-\frac{ln(u)}{2} +c[/tex]

=[tex]ln(v^2-1)-\frac{ln(v^2)}{2}+c[/tex]

Right hand side:

[tex]=-ln(x)[/tex]

Solve for v:

[tex]v=-\frac{-c_{1}+\sqrt{c_{2}+4x^2 } }{2x} \ or \ \frac{-c_{1}+\sqrt{c_{2}+4x^2 } }{2x}\\[/tex]

[tex]y=\frac{-1}{2} \sqrt[]{4x^2+4c_{1}^2} -c_{1}\ or \ \frac{1}{2} \sqrt[]{4x^2+4c_{1}^2} -c_{1}[/tex]


Related Questions

A report describes the results of a large survey that was conducted for the Center for Disease Control (CDC). The sample was selected in a way that the CDC believed would result in a sample that was representative of adult Americans. One question on the survey asked respondents if they had learned something new about a health issue or disease from a TV show in the previous 6 months. Data from the survey was used to estimate the following probabilities, where

L = outcome that a randomly selected adult American reports learning something new about a health issue or disease from a TV show in the previous 6 months
and
F = outcome that a randomly selected adult American is female
Data from the survey were used to estimate the following probabilities:

P(L)= 0.58 P(F)= 0.50 P(L and F)= 0.31

Are the outcomes L and F independent? Use probabilities to justify your answer.

Answers

Answer:

Since [tex]P(L \cap F) \neq P(L)P(F)[/tex], the outcomes L and F are not independent.

Step-by-step explanation:

Independent events:

Two events, A and B are independent, if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Are the outcomes L and F independent?

We are given that:

[tex]P(L \cap F) = 0.31[/tex]

Multiplication of the probabilities:

[tex]P(L)P(F) = 0.58*0.5 = 0.29[/tex]

Since [tex]P(L \cap F) \neq P(L)P(F)[/tex], the outcomes L and F are not independent.

How much will the class members earn if they spend six weeks doing yard work? How much will they earn if they spend six weeks having a car wash

Answers

For 6 weeks of yard work they’ll earn 3(320) or $960
For 6 weeks of car washed they’ll earn 1.5(700) or $1050

I got the 3 and the 1.5 by dividing 6 by the number of weeks on the table so 6/2 is 3 and 6/4 is 1.5

How many miles will Mrs. Garcia drive in eight hours if she is traveling 65 mph? _ miles

Answers

Answer:

she would probably drive 520 miles in she is driving 65 mph for a whole 8 hours

Step-by-step explanation:

Answer:

520

Step-by-step explanation:

This is a very simple explanation.

Mrs. Garcia drives eight hours...at 65mphs throughout the trip.

How many miles has she drove?

All you need to do is multiply 8x65 and you will get 520.

Mrs. Garcia drove a total of 520 miles.

Help! I’ll reward brainest its pretty easy

Answers

add the two fractions together
1/2 + 1/8 (can’t see properly, is it an 8)
1/8 + 1/8
4/8 + 1/8
=5/8

Which statements describe valid ways to rewrite a percent as a fraction? Check all that apply.
Write a fraction using the percent over 10 and simplify.
Write a fraction using the percent over 100 and simplify.
Divide the percent by 100, write it as a fraction, and simplify.
Multiply the percent by 100, write it as a fraction, and simplify.

Answers

Answer:

Write a fraction using the percent over 100 and simplify. AND. Divide the percent by 100, write it as a fraction, and simplify.

Step-by-step explanation:

Let's test all the answers and see which statements are true.

Let's just use 50 as the percent to test it. These statements should end up looking like [tex]\frac{1}{2}[/tex]

Write a fraction using the percent over 10 and simplify.

[tex]\frac{50}{10} =5[/tex], half of ten is 5, so this makes it invalid.

Write a fraction using the percent over 100 and simplify.

[tex]\frac{50}{100} =\frac{1}{2}[/tex], this is valid.

Divide the percent by 100, write it as a fraction, and simplify.

[tex]\frac{50}{100} =\frac{1}{2}[/tex], valid!

Multiply the percent by 100, write it as a fraction, and simplify.

[tex]50*100=500[/tex], invalid.

The two valid statements are: Write a fraction using the percent over 100 and simplify. AND. Divide the percent by 100, write it as a fraction, and simplify.

Answer:

abc

Step-by-step explanation:

c) 20 blank CD-Roms cost £3.20
How much do 75 CD-Roms cost?

Answers

Answer:

the cost of 75 CD Roms is £12

Step-by-step explanation:

The computation of the 75 CD roms cost is shown below:

Since it is mentioned that

for 20 blank CD roms it cost £3.20

So for 75 CD Roms, the cost would be

= £3.20 × 75 ÷ 20

= £12

Hence, the cost of 75 CD Roms is £12

Help!! Pythagorean theorem

Answers

Answer:

The Pythagorean theorem only works for right triangles. This is not a right triangle.

x = 23

All interior angles of a triangle = 180 degrees.

 A  +      B      +     C    + 180

(3x) + (2x+12) + (2x+7) = 180

7x + 19 = 180

7x = 161

x = 23

A = 3(23) = 69 degrees

B = 2(23) + 12 =58 degrees

C = 2(23) + 7 = 53 degrees

Answer:

x=23

Step-by-step explanation:

u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

Brenda sells necklaces at the 23rd Street Flea market. It costs her $10.00 in materials to make the necklaces. She decides to mark-up the price of her ned
by 75% to make a profit. An hour before the flea market closes she decided to reduce the leftover necklaces by 20% from the morning's price. How much
she selling her necklaces at the end of the day?
$20.00

Answers

Answer:

$ 14.00

Step-by-step explanation:

10 · 1.75 = 17.50

17.50 · .20 = 3.5

17.50 - 3.50 = 14.00

good luck, i hope this helps :)

Use the distributive property to write an equivalent expression. (6+8)x 2​

Answers

28 is the correct answer

3. Mrs. Hilt has a pizza that is 35 inches in diameter. What is the radius of that pizza?

Answers

17.5 inches

Radius is half of diameter so just do this process:

35/2 = 17.5

I seriously need help with this. I pay attention in class it's just so confusing!! I'm giving extra points. Now 15. Please tell the truth <3

Answers

Answer:

D

Step-by-step explanation:

Its D because A is all 90 degrees

Not C because all 90

I don't know what to do ​

Answers

120°, thinking logically it’s bigger than 90° but not big enough to be over 150°, so your last answer is 120°
That’s a 120 degree

PLEASE HELP IF POSSIBLE, ASAP!!!!!!!! :)

Answers

The Sum of all 3 needs to equal 1

A. 1/9 + 1/2 + 1/3 = 17/18

B. 1/9 + 2/9 + 1/3 = 6/9 = 2/3

C. 1/6 + 3/9 + 1/3 = 3/18 + 6/18 + 6/18 = 15/18

D. 2/9 + 8/18 + 1/3 = 4/18 + 8/18 + 6/18 = 18/18 = 1

The answer is D

PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((

Answers

Yes 1,6 is a solution

Five houses in the neighborhood sold this month for the following prices:
$328,000, $297,500, $415,000, $389,000, $345,000.
The house with the highest selling price sold for how much more than the median selling price?

Answers

Answer:

70,000

Step-by-step explanation:

Median= 345,000

Higest selling house= 415,000

415,000-345,000= 70,000

How do u turn 4 into a fraction

Answers

Answer:

4/1

Step-by-step explanation:

Multiply both the numerator and denominator by the value you chose in step 2. So to turn the whole number 4 into halves, you would multiply 4/1 by 2/2 and reach a value of 8/2. This completes the conversion of the whole number four into a fraction.

Answer:

4/1

Step-by-step explanation:

u put it over 1. Any whole number over one is considered a fraction, but its still the same number.

In a school of 330 students, 85 of them are in the drama club,
200 of them are in a sports team and 60 students do drama and sports.
Find the probability that a student chosen at random isn't in the drama club
or in a sports team.
You may wish to complete the Venn diagram to help you.
E
Drama
Sports
Question Feedback

Answers

Answer:

7/22

Step-by-step explanation:

From the question given above, the following data were:

Drama n(D) = 25

Sport n(S) = 140

Both drama and sport n(DnS) = 60

Not in drama or sport n(DnS)ᶜ = 105

Total or sample space n(S) = 330

Probability of not in drama or sport P(DnS)ᶜ =?

The probability that the student chosen is not in drama or sport can be obtained as follow:

P(DnS)ᶜ = n(DnS)ᶜ / nS

P(DnS)ᶜ = 105 / 330

Express the above to its lowest terms

P(DnS)ᶜ = 7/22

Therefore, the probability that the student chosen is not in drama or sport is 7/22

help me please asap!!!

Answers

Answer:

122°

Step-by-step explanation:

<ADC is an inscribed angle and its measure is equal to half of the arc it sees (minor arc AC)

if ADC is 61° then minor arc AC is 2 × 61 = 122

ABC is the center angle and so its measure is equal to the arc it sees which is 122°

I need help doing this please

Answers

it is super blurry can you put it by light

Step-by-step explanation:

what is the question asking

Use the number line to complete the statements.
The opposite of 4 is ____.
(1). -8
(2). -4
(3). 0
(4). 4
The opposite of –8 is _____.
(1). -8
(2). 0
(3). 4
(4). 8

Answers

Answer:

(2). -4

(4). 8

Step-by-step explanation:

The opposite of a negative or positive number will always be it's absolute value.

Formula for area the area of a triangle

Answers

I think A=12bh I hope it’s right

Write the expression 12 x 4^2 in words

Answers

Answer and Step-by-step explanation:

Twelve times four squared.

This is how you would write the expression in word format.

#teamtrees #PAW (Plant And Water)

Answer:

Twelve times four squared.

Step-by-step explanation:

I need the answer please help

Answers

Answer:

Check pdf

Step-by-step explanation:

what is the median of 6 8 10 12 12 15 15 20?​

Answers

Answer:

I think is 12..........

Answer:

It‘s either 12 or 12.5

Step-by-step explanation:

1. Lisa drives her car 46 km south and then 13 km east.
How far is she from her starting point?
Show work

Answers

Umm maybe 59 kilometers

Write the fraction 1/5 as a percent.

Answers

Answer:

20%

Step-by-step explanation:

13 + 4 (2x + 5)

Help pls

Answers

Answer:

8x + 33

Solution:

13 + 4 (2x+5)

4 • 2x = 8x

4 • 5 = 20

20 + 15 = 33

8x + 33 Is your answer

Can someone help me I don’t know how to do this it’s hard and confusing me

Answers

9514 1404 393

Answer:

increasing on 0 < x < 2f(2) = 4decreasing on 2 < x < 5

Step-by-step explanation:

You need to know that an even function is symmetrical about the y-axis. The graph to the right of the y-axis is the mirror image of the graph to the left. With that in mind, the questions are easily answered.

It might help to draw the function graph, as we did in the attached. Then it is more straightforward to see what is happening in each of the intervals.

The function is increasing in the interval 0 < x < 2.

The function value at x=2 is 4: f(2) = 4.

The function is decreasing in the interval 2 < x < 5.

Which number line shows the solution to the inequality 9x-4<5? I NEED IT ASAP PLSS free 15 points

Answers

Answer:

B would be your answer I think Don't hold me to it!

Step-by-step explanation:

Answer:B -4-2 0 2 4

Step-by-step explanation:

Another game you’ve set up at casino night involves rolling a fair six-sided die followed by tossing a fair coin. In this game, players earn points depending on the number they get on the die and which side of the coin turns up. For example, the player earns 5 points for getting (2, tails) Question 5 Find the probability that the outcome is either tails with any number, or heads with a number grater than 1

Answers

Answer:

tails with any number is 1/2, heads with greater than 1 is .4125

Step-by-step explanation:

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