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
sukhopar [10]
3 years ago
12

Write down a differential equation of the form dy/dt = ay + b whose solutions have the required behavior as t → ∞. all other sol

utions diverge from y = 2.

Mathematics
1 answer:
nordsb [41]3 years ago
6 0

The ODE has an equilibrium point at

\dfrac{\mathrm dy}{\mathrm dt}=ay+b=0\implies y=-\dfrac ba

We want y=2 to be an unstable equilibrium solution - in other words, we want all solutions with initial condition y(t_0)=c for c near 2 to diverge from y=2 - so -dfrac ba=2.

Divergence from y=2 would require that for y>2, any solution is increasing, and for y, and solution is decreasing. In order for that to happen, we need

\dfrac{\mathrm dy}{\mathrm dt}=ay+b>0\implies y>-\dfrac ba

if y>2, and

\dfrac{\mathrm dy}{\mathrm dt}=ay+b

if y.

Now we just pick a,b to satisfy these conditions. An easy choice is a=1, which forces b=-2, so that one possible ODE would be

\dfrac{\mathrm dy}{\mathrm dt}=y-2

I've attached a plot of the slope field to demonstrate the behavior of the solutions.

You might be interested in
Share 35$ in the ratio 4:1
ZanzabumX [31]

35/5= 7

so,

4*7 = 28                          1*7= 7


The answer is  28:7

5 0
3 years ago
help please lol, Which pizza company has the better deal for Isaac and how much money will it cost him
Brilliant_brown [7]

the left one is the  answer

8 0
3 years ago
Claudia is reading a book that has 360 pages. she read some book last week. She plans to read 46 pages today when she does she w
tangare [24]
4/5 of 360 is 288, but that's how much she read after today so last week she read that much minus 46 which is 242
7 0
3 years ago
Read 2 more answers
5(2^(2x+7)) How do you solve this equation??
Liono4ka [1.6K]
Simplifying
0x + 7 + 5x = 2x + 30 + 40

Anything times zero is zero.
0x + 7 + 5x = 2x + 30 + 40

Combine like terms: 0 + 7 = 7
7 + 5x = 2x + 30 + 40

Reorder the terms:
7 + 5x = 30 + 40 + 2x

Combine like terms: 30 + 40 = 70
7 + 5x = 70 + 2x

Solving
7 + 5x = 70 + 2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.
7 + 5x + -2x = 70 + 2x + -2x

Combine like terms: 5x + -2x = 3x
7 + 3x = 70 + 2x + -2x

Combine like terms: 2x + -2x = 0
7 + 3x = 70 + 0
7 + 3x = 70

Add '-7' to each side of the equation.
7 + -7 + 3x = 70 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 70 + -7
3x = 70 + -7

Combine like terms: 70 + -7 = 63
3x = 63

Divide each side by '3'.
x = 21

Simplifying
x = 21
3 0
3 years ago
What method did you use? Why? Solve. for x: 47° 13​
Kazeer [188]

Answer:

Step-by-step explanation:

Givens

You have the hypotenuse: 13

You seek the adjacent side: x

You have the angle enclosing the 2: 47 degrees.

The relationship is the Cosine

Solution

Cos(47) = opposite / hypotenuse

Cos(47) = 0.6820                            From your calculator

Cos(47) = x / 13                                Multiply both sides by 13

13*cos(47) = x

x=8.866

7 0
3 years ago
Other questions:
  • (01.01) Kisha and Rae are asked to solve −5x − 14 = 2x + 7. Identify where one of them made an error.
    15·2 answers
  • The perimeter of a chalkboard is 16 feet. The area is 15 square feet. What are the dimensions of the board
    11·1 answer
  • If a and b are odd integers, then a – b is an even integer.
    12·2 answers
  • What is the area of the partial circle with a radius of 8 cm?
    15·2 answers
  • Rationalize the denominator of the following expression and simplify:
    8·1 answer
  • AP:2,x,26.<br> Find the value of x
    8·1 answer
  • Could someone please solve this and explain how to do it?
    12·1 answer
  • What is point A on the coordinate plane
    5·2 answers
  • What percentage of people has an IQ score less than 83 or greater than 117
    15·1 answer
  • Using the Addition Method, solve for x in the following system of linear equations.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!