1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mojhsa [17]
3 years ago
10

I need help with this homogeneous equation

Mathematics
1 answer:
slamgirl [31]3 years ago
6 0

Answer:

ln [1 - (\frac{y}{x} )^{2} ] + ln x + c = 0. This is the solution.

Step-by-step explanation:

The homogeneous differential equation is given by  

\frac{dy}{dx} = \frac{x^{2} + y^{2} }{2xy}

⇒ \frac{dy}{dx} = \frac{1 + (\frac{y}{x} )^{2} }{2(\frac{y}{x} )} ........ (1)

Now to solve this differential equation we assume that y = vx where v is another variable.

So, differentiating with respect to x we get \frac{dy}{dx} = v + x \frac{dv}{dx}

Therefore, the above equation (1) becomes

v + x \frac{dv}{dx} = \frac{1 + v^{2} }{2v} {Since v = \frac{y}{x}}

⇒ x\frac{dv}{dx} = \frac{1 + v^{2} - 2v^{2}  }{2v}

⇒ x\frac{dv}{dx} = \frac{1 - v^{2}}{2v}

⇒ \frac{2v}{1 - v^{2} } dv = \frac{dx}{x} {By separation of variables}

Now, integrating both sides we get,

\int {\frac{2v}{ 1- v^{2}}} \, dv = \int {\frac{dx}{x} } \, dx

⇒ - \int {\frac{d(1 - v^{2} )}{1 - v^{2}}}  = \int {\frac{dx}{x} }

⇒ - ln (1 - v^{2}) = ln x + c {Where c is the integration constant}

⇒ ln [1 - (\frac{y}{x} )^{2} ] + ln x + c = 0 (Answer)

You might be interested in
11. In your own words, describe how to view the
astraxan [27]
Do they want me describe the step by step process or no???
5 0
3 years ago
Plz help plz plz plz plz
Likurg_2 [28]

Answer:

4

Step-by-step explanation:

The ratio of green : pink = 32 : 56 = 4 : 7

After 7 pink are given away, then

ratio = ? : 49 = 4 : 7 ← ratio has to be the same

Using proportion

\frac{?}{4} = \frac{49}{7} ( cross- multiply )

7? = 196 ( divide both sides by 7 )

? = 28

Thus the ratio = 28 : 49 = 4 : 7

Thus 32 - 28 = 4 green should be given

3 0
3 years ago
What is the 87th term of the arithmetic sequence with this explicit formula
emmasim [6.3K]

Answer:Step-by-step explanation:

If there is a sequence and if we are to find its 87th term we must have the general term formula for the sequence.

Normally for sequences which follow a pattern there will be a formula for nth term.

Example is arithmetic sequence nth term = a+(n-1)d where a is the I term and d the common difference.

Similarly for geometric sequence nth term

= is the nth term

Thus to find the 87th term, we must be able to find out the pattern of the sequence by which any term is related to its previous term

Either general term formula or recurring formula should be given to get the 87th term

Step-by-step explanation: is arithmetic sequence nth term = a+(n-1)d where a is the I term and d the common difference. Still stuck? Get 1-on-1 help from an expert tutor now.

8 0
2 years ago
What percent of 42 is 28
oksian1 [2.3K]
So if you take 42/100 you get .42
Then you take .42 and multiply it by 28
Giving you the answer of 11.76
3 0
3 years ago
Read 2 more answers
For what value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution
hodyreva [135]

The value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution is -5/2

<h3>System of equation</h3>

For a system of equation to have no solution, the expression on both sides must be different.

Given the system of equation

6x-5y=3 and

3x+ay=1

For the equations to have no solution, the a1/a2= b1/b2

Substitute

6/3 = -5/a


Cross multiply

2 = -5/a

a= -5/2

Hence the value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution is -5/2

Learn more on system of equation here: brainly.com/question/14323743

#SPJ1

5 0
2 years ago
Other questions:
  • Can somebody please help me with this paper for math hw
    8·1 answer
  • Which ratio is equivalent to 18/36​
    7·1 answer
  • How can you determine whether a number is a solution of an equation ?
    13·1 answer
  • Hudson bought several cans of tennis balls. Each contained both green and yellow tennis balls. He purchased 10 green tennis ball
    8·1 answer
  • The surface area of an oil spill gets 105% larger every day, represented by the function s(x) = (1.05)x − 1. On the first day, i
    8·1 answer
  • What is the sum of –356.1 + 258.6
    5·2 answers
  • Need Answer ASAP! 30 POINTS !
    9·2 answers
  • An average clementine is shaped like a sphere and has a dismeter of 3.5 inches. What is the volume of the fruit? Round your answ
    13·1 answer
  • Please read the caption! Thanks!! Pls help me :)))
    13·1 answer
  • 81 + 7x² +8yt-sx<br> if x = 2 what is the answer
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!