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
Misha Larkins [42]
3 years ago
12

Solve: dy/dx − 2xy = x, with y(0) = 0.

Mathematics
1 answer:
JulijaS [17]3 years ago
8 0

Answer:

1 + 2y = x^2

Step-by-step explanation:

Given differential equation,

\frac{dy}{dx}-2xy=x

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

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

\frac{dy}{1+2y}=xdx

Integrating both sides,

\int \frac{dy}{1+2y}=\int xdx----(1)

Put 1 + 2y = u

Differentiating both sides,

2dy = du

\implies dy=\frac{du}{2}

From equation (1),

\frac{1}{2} \int \frac{du}{u}=\int xdx

\frac{1}{2}\log u = \log x + C

\frac{1}{2} \log (1+2y)=\log x+C---(2)

If x = 0, y = 0

\implies C=0

From equation (2),

\frac{1}{2} \log(1+2y)=log x

\log (1+2y) = 2\log x

\log (1+2y) = \log x^2

\implies 1 + 2y = x^2

You might be interested in
Please Help Can weather and climate be used interchangeably.
pickupchik [31]

Answer:

yes

'Weather' and 'climate' are used interchangeably.

Step-by-step explanation:

"Climate" describes the average atmospheric conditions over many years

the average annual rainfall, the predominant wind direction, or the season in which rain is likely to occur can be said as  Weather

<h2><u><em>hope it helps u</em></u></h2><h2><u><em>if it does so please mark me as brainiest </em></u></h2>
8 0
3 years ago
Read 2 more answers
How many tens are in 700?
scoray [572]

Answer:

70

Step-by-step explanation:

700 / 10 = 70

5 0
3 years ago
Read 2 more answers
I NEED THIS ANSWER QUICK (5 1/6 - x) ∙ 2.7 - 5 3/4 = -1.25 what is x
fgiga [73]

Answer:

  x = 3 1/2

Step-by-step explanation:

You could simplify the given equation first, then solve the resulting 2-step linear equation. It might work better to undo the operations done to the variable.

<h3>Solution</h3>

  (5 1/6 -x)(2.7) -5 3/4 = -1 1/4 . . . . . given

  (5 1/6) -x)(2.7) = 4 1/2 . . . . . . . add 5 3/4 to both sides

  (5 1/6 -x) = 4.5/2.7 = 5/3 . . . divide by 2.7

  31/6 -10/6 = x . . . . . . . . . . add x-5/3, use common denominators

  21/6 = x = 7/2

  x = 3 1/2

6 0
2 years ago
What is 33% out of 50
Zolol [24]

Answer:

66

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
I have no idea how to do this.
Alex17521 [72]

Answer:

<2 = 133°

Step-by-step explanation:

< beside <2 = 47

<2 + < beside <2 =180 (straight line)

<2 + 47 =180

<2 = 180-47

<2 = 133°

3 0
2 years ago
Other questions:
  • Riley has 3 5/9 gallons of fuel left in his car. He uses 7/16 of the fuel to drive to the bank. Then, he uses 2/5 of the remaini
    12·2 answers
  • -5s=21.5 how do solve it
    11·1 answer
  • Y-intercept = 4.5 and slope = -2.5<br> equation: y =<br> X +
    12·1 answer
  • Help? Thanks!!!!!!!!!!!
    6·1 answer
  • In the coordinate plane, when you move an ordered pair (x,y) to the right, _______
    12·1 answer
  • Given that f(x) = 3x + 5, find f(x + 2)
    13·1 answer
  • A construction company built a scale model of a new building. the model was built usinga scale of 3 inches= 32 feet. if the buil
    14·1 answer
  • Need help, Iĺl give brainliest &lt;3
    11·2 answers
  • Show work for number one please!
    8·1 answer
  • If 14x + 5 = 12, what is the value of x?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!