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
never [62]
3 years ago
9

Xy′ = √(1 − y2 ), y(1) = 0

Mathematics
1 answer:
Ulleksa [173]3 years ago
7 0

Answer:

The particular solution is y=\sin (\ln|x|) .

Step-by-step explanation:

The given differential equation is

xy'=\sqrt {1-y^2}

It can be written as

x\frac{dy}{dx}=\sqrt {1-y^2}

Use variable separable method to solve the above equation.

\frac{dy}{\sqrt {1-y^2}}=\frac{1}{x}dx

Integrate both sides.

\int \frac{dy}{\sqrt {1-y^2}}=\int \frac{1}{x}dx

\sin^{-1} y=\ln|x|+C            .... (1)

It is given that y(1)=0. It means y=0 at x=1.

\sin (0)=\ln|1|+C

0=0+C

0=C

The value of constant is 0.

Substitute C=0 in equation (1) to find The required equation.

\sin^{-1} y=\ln|x|+0

Taking sin both sides.

y=\sin (\ln|x|)

Therefore the particular solution is y=\sin (\ln|x|) .

You might be interested in
Tamara invests $8000 in two different accounts. The first account has a simple interest rate of 3% and the second account has a
34kurt

Let Tamara invests amount X in 3% account. She invests 8000-X in 2% account.

The interest after t years is given by

I=Prt. After 1 year the two interests are equal, that is

X(\frac{3}{100}) (1)=(8000-X)(\frac{2}{100}) (1)\\ 3X=2(8000-X)\\ 5X=16000\\ X=3200

Thus, Tamara has to invest \$3200 in 3% account and \$8000-\$3200=\$4800 in 2% account.

4 0
3 years ago
A dinner is served at a wildlife fundraiser. The constant relationship between the number of people served at dinner n and the n
Leya [2.2K]

Answer:

C=4n

im sure this is the correct one

3 0
3 years ago
Read 2 more answers
choose a random number between 1 and 20 . What is the probability that the number is greater than 5 and less than 15
erma4kov [3.2K]

Answer:

MY RANDOM ANSWER : my answer is 3

Step-by-step explanation:

The probablitiy of that is 9

8 0
2 years ago
_ divided by 4= _ remaider 5
vagabundo [1.1K]

Answer:

20 / 4 =5

Step-by-step explanation:

I think

4 0
3 years ago
How many litres of oil are in the tank
Naddika [18.5K]

Answer:

24,649 liters

Step-by-step explanation:

V = pi * h * r^2

V = pi * 250 * 100^2

V = 3.14 * 7850000

= 24,649,000 cm^3

1 liter =. 1000 cm3

X. =. 24,649,000 (cross multiplication)

24,649,000/1000=24,649 liters

7 0
3 years ago
Other questions:
  • On a coordinate plane, a curved line crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 0.25). The line exits t
    7·2 answers
  • Cqn someone answer this?​
    15·2 answers
  • 1-4<br> Will give brainliest!!!!<br><br> Pls show work!!
    9·2 answers
  • Water weighs 62.4 pounds per cubic foot. How much does the water in a tank that measures 7 ft × 4 ft × 9 in, weigh?
    12·2 answers
  • Ill freind you on Fortnite just give me epic name
    11·2 answers
  • 5y + 3 = 8y − 5 + 2y
    13·2 answers
  • Help pls if u know, what are the coordinates
    12·1 answer
  • Which expressions are equivalent to (13x−4x−53x)−(−13x−3) ?
    9·2 answers
  • 2x + 5y = 14 4x + 2y = -4 solving with elimination​
    5·2 answers
  • Lillian went shopping for a new phone because of a sale. The price on the tag was $20, but Lillian paid $16 before tax. Find the
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!