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
notsponge [240]
3 years ago
13

Consider the following homogeneous differential equation. y dx = 2(x + y) dy Use the substitution x = vy to write the given diff

erential equation in terms of only y and v.
Mathematics
1 answer:
astra-53 [7]3 years ago
4 0

Answer:

ydv = (v +2)dy\\            

Step-by-step explanation:

We are given the following differential equation:

y dx = 2(x + y) dy

We have to substitute

x = vy

Differentiating we get,

\dfrac{dx}{dy} = v + y\dfrac{dv}{dy}

Putting value in differential equation, we get,

y dx = 2(x + y) dy\\\\y\dfrac{dx}{dy}=2(x+y)\\\\y(v+y\dfrac{dv}{dy}) = 2(vy + y)\\\\vy + y^2\dfrac{dv}{dy} = 2vy +2y\\\\y^2\dfrac{dv}{dy}=vy +2y\\\\y^2dv = y(v+2)dy\\ydv = (v +2)dy\\

is the differential equation after substitution.

You might be interested in
Lee purchased groceries for $33.29. He paid with two $20 bills. How much change should Lee receive?
Pachacha [2.7K]

Answer: $6.71

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Please help me on this question asap!
alekssr [168]

Answer:

see explanation

Step-by-step explanation:

ΔABE and ΔACD are similar hence the ratios of corresponding sides are equal, that is

\frac{AB}{AC} = \frac{AE}{ED} = \frac{BE}{CD}

Using the first pair of ratios then

\frac{20}{5} = 4 = \frac{26}{ED}, hence

4ED = 26 ( divide both sides by 4 )

ED = 6.5 cm

------------------------------------------------------------------

(b)

Similarly

\frac{BE}{18} = 4, hence

BE = 4 × 18 = 72 cm

4 0
3 years ago
H + 6.9 =11.4<br><br> h= <br><br><br> What is h
Zinaida [17]
h+6.9=11.4 \\ &#10; \\ 11.4-6.9=4.5 \\ &#10; \\ h=4.5
4 0
3 years ago
1. The ice cream shop offers a choice of a 3 cone sizes, 15 flavors, and 8
Aliun [14]

Answer:

3 x 15 x 8 = 360

so, if there were 3 cone sizes, 25 flavors of ice cream, and 8 toppings, there would be about 360 different operations

5 0
3 years ago
You are calculating the volume of a box which has a width ofx inches, a
madreJ [45]

Using limits, it is found that the end behavior of the polynomial function for the volume of the rectangular box is:

B. down and up.

<h3>What is the volume of a rectangular prism?</h3>

The volume of a rectangular prism of length l, width w and heigth h is given by:

V = lwh.

In this problem, we have that the dimensions are given by:

  • w = x.
  • l = x - 1.
  • h = x - 2.

Hence the volume is given by:

V = x(x - 1)(x - 2) = x(x^2 - 3x + 2) = x^3 - 3x^2 + 2x

<h3>What is the end behavior of a function?</h3>

It is given by it's <u>limits as x goes to infinity</u>.

Hence:

\lim_{x \rightarrow -\infty} V(x) = \lim_{x \rightarrow -\infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow -\infty} x^3 = -\infty

\lim_{x \rightarrow \infty} V(x) = \lim_{x \rightarrow \infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow \infty} x^3 = \infty

Which means that option B is correct.

More can be learned about limits at brainly.com/question/22026723

7 0
3 years ago
Other questions:
  • A 5 -ounce can of tuna cost $0.90. A 12- ounce can of tuna cost $2.40. which is the better buy?
    13·1 answer
  • Answer plzzzzzzzzzzzzzzzzzz
    9·1 answer
  • Which equation shows the same relationship as 4=1/5x20
    7·1 answer
  • Here is the histogram of a data distribution. All class widths are 1.
    7·1 answer
  • . 551.2: 2.08 =<br> -<br> Answe???
    9·1 answer
  • Two triangular faces of a rectangular pyramid each have an area of 7.8 cm and the other two faces each have an area of 16.5
    9·2 answers
  • PLEASE HELP ASAP WILL MARK BRAINLIEST
    6·1 answer
  • A sweatshirt is $67.50, if
    10·2 answers
  • If r is the midpoint of AB and AR=14, then AB=______
    14·1 answer
  • Consider the functions: f(x) = x2 + 4x – 1 and g(x) = 2x + 5. See graphs alongside. a) Identify each curve b) Find the coordinat
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!