Solve the differential equation (2x+y)dx+(x−2y)dy = 0

Answers

Answer 1

Answer:

y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))

Step-by-step explanation:

Solve 2 x + y(x) + (dy(x))/(dx) (x - 2 y(x)) = 0:

Let P(x, y) = 2 x + y and Q(x, y) = x - 2 y.

This is an exact equation, because (dP(x, y))/(dy) = 1 = (dQ(x, y))/(dx).

Define f(x, y) such that (df(x, y))/(dx) = P(x, y) and (df(x, y))/(dy) = Q(x, y).

Then, the solution will be given by f(x, y) = c_1, where c_1 is an arbitrary constant.

Integrate (df(x, y))/(dx) with respect to x in order to find f(x, y):

f(x, y) = integral(2 x + y) dx = x^2 + x y + g(y) where g(y) is an arbitrary function of y.

Differentiate f(x, y) with respect to y in order to find g(y):

(df(x, y))/(dy) = d/(dy) (x^2 + y x + g(y)) = x + (dg(y))/(dy)

Substitute into (df(x, y))/(dy) = Q(x, y):

x + (dg(y))/(dy) = x - 2 y

Solve for (dg(y))/(dy):

(dg(y))/(dy) = -2 y

Integrate (dg(y))/(dy) with respect to y:

g(y) = integral-2 y dy = -y^2

Substitute g(y) into f(x, y):

f(x, y) = x^2 - y^2 + y x

The solution is f(x, y) = c_1:

x^2 - y^2 + y x = c_1

Solve for y:

y(x) = 1/2 (x - sqrt(5 x^2 - 4 c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 - 4 c_1))

Simplify the arbitrary constants:

Answer:  y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))


Related Questions

A bag contains 15 marbles. Six are red, three are blue, and the rest are green or yellow. If the ratio of green marbles to blue marbles is 2 to 3, what is the ratio of yellow marbles to red marbles?

Question 2 options:

3/6


4/6


4/15


6/4
ill give brain for the first one

Answers

Answer:

3/6

Step-by-step explanation:

15 - (6+3) = 6

6 ÷ 2 = 3

number of red is 6

and green is 3

3/6

One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 45 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.

Answers

Answer:

the largest angle are 90 degree

Step-by-step explanation:

let x is the smallest angle

the angles are

x+x+2x=180

4x=180

4x/4=180/4

x=45 degree

2x=90

Smallest angle = x
Largest angle = 3x
Third angle = 45 + x

x + 3x + 45 + x = 180
5x + 45 = 180
5x = 180 - 45
5x = 135
x = 135/5
x = 27

Largest angle = 3x = 3 x 27 = 81 degree

The 6 games Kelly's team played took a total of 7 hours. How many minutes total did they play softball?​

Answers

There is 420 minutes in 7 hours.
1 hour = 60 minutes
60 times 7 would be 420

andrei has a glass tank. first he wants to put in some marbles, each of which has a volume of 0.04 liters. the, he wants to fill the tank with water until its completely full. if he uses 50 marbles he will have to add 33 liters of water,


what is the volume of the tank?

Answers

Answer:

  35 liters

Step-by-step explanation:

The volume of 50 marbles will be ...

  50 × 0.04 L = 2.00 L

Adding 33 liters of water to that volume of marbles will bring the total volume of material in the tank to ...

  2 L + 33 L = 35 L . . . . volume of full tank

simplify the surd square root 12 x square root 8

Answers

The simplification of square root 12 x is [tex]\mathbf{2 \sqrt{3x}}[/tex] and the square root of 8 is [tex]\mathbf{2 \sqrt{2}}[/tex]

What is Surds?

Surds is a mathematical expression of numbers in square roots that cannot be changed to real numbers but be further simplified into irrational numbers.

From the given information.

The simplification of [tex]\mathbf{\sqrt{12x}}[/tex] is:

[tex]\mathbf{= \sqrt{4 \times 3x }} \\ \\ \mathbf{= 2\sqrt{ 3x }}[/tex]

The simplification of the  [tex]\mathbf{\sqrt{8 }}[/tex] is determined by factoring 8:

i.e.

[tex]\mathbf{= \sqrt{4 \times2 }} \\ \\ \mathbf{= 2\sqrt{ 2}}[/tex]

Learn more about surds here:

https://brainly.com/question/24700530

2(4x - 8y) - 9x + 7 as a simplifying expression.

Answers

Answer:

2(4x - 8y) - 9x + 7

8x - 16y - 9x + 7

-1x - 16y + 7

1 What is the remainder when 245 is divided by 9?
2 A bridge in the park is 84 feet long. The length of the bridge is 6 times the width of the bridge. How wide is the bridge?
3 Dylan gets home from school at 4:05 p.m. He spends 20 minutes on his homework and 15 minutes practicing the drums. How many minutes does he have left before leaving for soccer practice at 5:15 p.m.?

Answers

Answer:

245÷9 =0 witt remainder 9

Obtain two numbers such their HCF is 20 and their LCM is 300....... By steps... ​Plzzzzzz answer fast

Answers

Answer:

60 and 100

Step-by-step explanation:

Look for 2 multiples of 20 which are also factors of 300

No long explanation needed

In a right triangular prism, the area of the triangular base is 50 square feet. The height of the prism is 12 feet. What is the volume of the prism?


A.220ft^3


B.600ft^3


C.100ft^3


D.135ft^3

Answers

Answer:600ft³ is the volume of the prism.SOLUTION:50×12= 600ft³

600 ft²

Solution:

Area of triangular prism - -

Formula's:

Area of the base * Height

Here the volume:

50 * 12

600 ft²

WILL GIVE BRAINLIEST!!!!

1. What is the length of BD?

Answers

Ansanswer choice b

Step-by-step explanation:

Identify the premise. Choose the correct answer below.
O A. Men are better qualified for high office than women.
B. Men in high office.
C. All the mayors of my hometown have been men.
© D. Mayors of a certain town.

Answers

it’s C. All the mayors of my hometown have been me.

Please help mark as brainliest​

Answers

Answer:

the answer is an group tens

Step-by-step explanation:

BRAINLIEST PLEASE

find the difference between the actual and estimated values of 55 - 21​

Answers

Answer:

Actual: 34 Estimated: 40

Step-by-step explanation:

The difference between these values is that the actual difference is more accurate. If you're asking for the difference as in subtracting, then 7 is the answer. Hope this helps :)

Answer:

6

Step-by-step explanation:

Actual values = 55 - 21

                         = 34

Estimated values = 60 - 20 = 40

Difference between actual and estimated values = 40 - 34 = 6

if Penelope's car has an average fuel consumption of 3 miles per gallon and she uses 9.5 gallons how far did she drive ​

Answers

Answer:

approximately 3.16 repeated

Step-by-step explanation:

Given parameters:

Average fuel consumption of Penelope's car = 3miles per gallon

Amount of fuel used = 9.5 gallons

Unknown:

Distance of her drive = ?

Solution:

  Since her rate of fuel consumption per miles is known, we can simply solve for the distance she covers.

  Distance covered = Rate of fuel consumption per miles x amount of fuel used

Distance covered  = 3  x 9.5  = 28.5miles

The distance covered by Penelope's car is 28.5miles


Find the sine ratio of angle -. Hint: Use the slash symbol (/ ) to represent the fraction
par, and enter the fraction with no spaces.

Answers

Answer:

4/5

Step-by-step explanation:

The sine ratio is defined as the opposite leg/hypotenuse.  The opposite leg is 4 and the hypotenuse is 5.

Find the L.C.M of the given pair of numbers using the prime factors method. 70 and 84​

Answers

Answer:

420

Step-by-step explanation:

Prime Number: a whole number greater than 1 that cannot be made by multiplying other whole numbers

First prime numbers: 2, 3, 5, 7, 11, 13, 17, ...

Prime Factorization: prime numbers that multiply together to make the original number.

LCM = least common multiple: smallest positive number that is a multiple of two or more numbers

Start by finding the prime factorization of each number.

Start with the smallest prime number: 2

70 ÷ 2 = 35

35 is not divisible by 2 or 3, but is divisible by 5:

35 ÷ 5 = 7

7 is a prime number, so cannot be divided any further

So  70 = 2 × 5 × 7

Start with the smallest prime number: 2

84 ÷ 2 = 42

Again divide by 2:

42 ÷ 2 = 21

Now divide by 3:

21 ÷ 3 = 7

So  84 = 2 × 2 × 3 × 7

Write each number as a product of primes, matching primes vertically when possible

84 = 2 × 2 × 3       × 7

70 = 2             × 5 × 7

Now bring down the primes in each column. The LCM is the product of these factors.

LCM = 2 × 2 × 3 × 5 × 7 = 420

if one cup of flour is $0.44, How much will 1/2 cup cost?

Answers

Answer:

$0.22

Step-by-step explanation:

$0.44 -1/2 cup = $0.22

Question 4 of 5
Select the correct answer.

Sebastian randomly surveyed 25 people in his neighborhood to find out which electric company they use. In his survey, he found that
16% of the sample use Reliable Energy

What would most likely happen if he decided to randomly survey 50 people instead?

A. There is not enough information to determine how the sample proportion would be affected.

B.The sample proportion would less closely model the population proportion.

C. The sample proportion would not be affected.

D The sample proportion would more closely model the population proportion.

Answers

Answer:

D The sample proportion would more closely model the population proportion.

Step-by-step explanation:

The more people surveyed, the more accurate the information.

2 inches is approximately 5 centimeters. Kevin is 66 inches tall. How many centimeters (cm) tall is he?

Answers

He is approximately 330 cm because 60 times 5 is 300 and 6 times 5 is 30. If you add it up it is 330 cm

A song has 12 beats every 5 seconds . How many beats are there in 30 seconds?

Answers

Answer:

72 beats

Step-by-step explanation:

sec    |   5      |     30

beats |   12     |     x

30 divided by 5 = 6

12 times 6 = 72

What is 94.239 rounded to the nearest thousandth?

Answers

it already is at it

94.239 is already rounded to the nearest thousand as the no. of digits after the decimal place is three.

What is rounding off of numbers?

We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, 94.239 rounded to the nearest thousandth it is already rounded to the nearest thousand the no. of digits after the decimal place is three.

learn more about rounding off numbers here :

https://brainly.com/question/1285194

#SPJ2

Evaluate 2d - 3n divided by four n = 2 and d = 3

Answers

Answer:

0 is your answer..........

The number of students attending the seventh grade class trip is 4 times the number of teachers attending. What Is tge ratio of teachers to studets attending the class trip?

Answers

Answer:

1:4

Step-by-step explanation:

pls heart and give brainliest much appreciated

Answer:

1:4

Step-by-step explanation:

1:4 ok bye, bc I needa ask sum questions so dont come 4 me

A triangle has sides with lengths of 60 feet, 63 feet, and 87 feet. Is it a right triangle?

Answers

Answer:

Yes

Step-by-step explanation:

We can use the Pythagorean Theorem to check if this triangle is a right triangle:

[tex]a^2+b^2=c^2[/tex]

Note that [tex]a[/tex] and [tex]b[/tex] are the legs of the triangle and [tex]c[/tex] is the hypotenuse:

Substitute the lengths of the sides into the equation:

[tex]60^2+63^2=87^2[/tex]

[tex]3600+3969=7569\\7569=7569[/tex]

Therefore this triangle is a right triangle.

Yes, hope this helps.

Which of the binomials below is a factor of this trinomial?

x^2 - 5x - 36

A. x - 7

B. x + 4

C. x^2 + 7

D. x - 4

Answers

answer:

B

Step-by-step explanation:

x² - 5x - 36 = (x - 9)(x + 4)

x² + (a + b)x + ab = (x + a)(x + b)

Which equation represents the relationship between the angles shown below?

Answers

Answer:

4x + 44 = 180

Step-by-step explanation:

4x = 180- 44

4x = 136

x= 136÷ 4

x= 34

Answer:

4x + 44 = 180

Step-by-step explanation:

sum of angles on a straight line = 180

4x + 44 = 180

subtract 44 from both sides

4x + 44 - 44 = 180 - 44

4x = 136

Divide both sides by the coeficient of x

4x = 136

4 4

x = 34

Please Help! locks in 30 min! Will give brainlest!

Answers

Answer:

First option [tex]0, \frac\pi2, \pi, \frac{3\pi}2[/tex]

Step-by-step explanation:

first of all, let's replace the lhs with the equivalent in sine (from the pythagoran identiy on sine and cosine)

[tex]1-sin^2\theta =1-sin\theta[/tex]

At this point we take 1 from both side, and change signs just out of convenience.

[tex]\sin^2\theta =sin\theta[/tex]

Now we have 2 options. If [tex]sin \theta =0 \leftrightarrow \theta = k\pi[/tex] the equation is verified, and we got two solutions [tex]\theta =0; \theta = \pi[/tex]. Else, we can divide by [tex]sin\theta[/tex] and we get

[tex]sin\theta = 1 \leftrightarrow \theta = \frac\pi2+k\pi[/tex].

We can add everything together and write

[tex]\theta = k\frac\pi2; k\in\{0,1,2,3\}[/tex] or, in our case, the first answer.

( THE SUM OF THE MEASURES OF THE ANGLES BELOW IS 180* ) I will give brainlst for whoever gets this right and fills it out

Answers

Answer:

2x-10+x+x+10=180, or 4x=180

Step-by-step explanation:

So since the total is 180, you add them all up like an equation.

So,

2x-10+x+x+10

Combine like terms

4x=180

x=45

Then plug it back in to the equations.

x=45

(2x-10)=80

(x+10)=55

In the figure below,
What is the value of x?

Answers

Answer: 16 degrees

Step-by-step explanation:

(3x - 18) = 66

Because vertically opposite angles are equal

66 - 18 = 48

48 divided by 3 = 16

PLEASE HELP!!!! TELL ME HOW TO DO IT

Answers

The answer I think is this
fx=x^2-3
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