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
alina1380 [7]
3 years ago
10

Find the general solution of (x+3)y’=2y

Mathematics
1 answer:
gregori [183]3 years ago
5 0

Answer:

y=C(x+3)^2

Step-by-step explanation:

We are given:

\displaystyle (x+3)y^\prime=2y

Separation of Variables:

\displaystyle \frac{1}{y}\frac{dy}{dx}=\frac{2}{x+3}

So:

\displaystyle \frac{dy}{y}=\frac{2}{x+3} \, dx

Integrate:

\displaystyle \int\frac{dy}{y}=\int\frac{2}{x+3}\, dx

Integrate:

\displaystyle \ln|y|=2\ln|x+3|+C

Raise both sides to e:

|y|=e^{2\ln|x+3|+C}

Simplify:

|y|=(e^{\ln|x+3|})^2\cdot e^C

So:

|y|=C|x+3|^2

Simplify:

y=\pm C(x+3)^2=C(x+3)^2

You might be interested in
Write your question here (Keep it simple and clear to get the best answer)4x³-5x is it odd or even function
Dvinal [7]

Answer:

odd

Step-by-step explanation:

To determine if odd/ even

• If f(x) = f(- x) then it is even

• If f(- x) = - f(x) then it is odd

Given

f(x) = 4x³ - 5x , then

f(- x) = 4(- x)³ - 5(- x) = - 4x³ + 5x

Since f(x) ≠ f(- x) then it is not even

- f(x) = - (4x³ - 5x) = - 4x³ + 5x

Since f(- x) = - f(x) , then 4x³ - 5x is odd

5 0
3 years ago
On a line graph, time is usually represented on the vertical axis. true or false?
777dan777 [17]
False, it is on the horizontal.
7 0
3 years ago
Read 2 more answers
20 points!!!!!!!!!!! HELP
satela [25.4K]
They’re right it’s B
7 0
3 years ago
Read 2 more answers
A store sells Brazilian coffee for $10 per lb. and Columbian coffee for $14 per lb. If the store decides to make a 150-lb. blend
Artemon [7]

Answer:

The store should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian cofee.

Step-by-step explanation:

Let "b" be the amount of Brazilian coffee, in pounds, required for the blend and "c" the amount of Colombian coffee required, in pounds.

Since there are two unknown variables a two-equation system is needed to solve the problem, we can set up one equation for weight and another for price as follows:

b+c=150\\10*b+14*c=11*150

Solve for "c" by multiplying the first equation by -10 and adding it to the second one:

b+c=150\\10b+14c -10b-10c=11*150 -(10*150)\\4c=150\\c = 37.5

Now, solve for b by replacing the value obtained into the first equation

b+c=150\\b= 150 - 37.5\\b=112.5

The store should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian cofee.

6 0
3 years ago
Add<br>3×+8y-12zand5x-7y+15z<br>help meee<br>​
inn [45]

3x+5x+12z+15z+8y+7y

8x+17z+15y

4 0
3 years ago
Other questions:
  • Emily is packing her bags for her vacation. She has 6 unique Fabergé eggs, but only 3 fit in her bag. How many different groups
    15·1 answer
  • This rectangular prism was constructed by placing unit cubes together without any gaps or overlaps.
    15·1 answer
  • Solve the system of equations given below y=-3x+6 and y =2x-4
    10·2 answers
  • For which of the following numbers doesn’t the 5 appear in the hundredths place? (Multiple answers) A. 152.76 B. 26.578 C 12.057
    7·1 answer
  • I don't quite understand this problem: 6+√44/2 (or 6 plus the square root of 44 over 2). I know the answer is 3+√11 (3 plus the
    6·1 answer
  • Brett has consumed 1,400 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily
    15·2 answers
  • If there are 624 calories in 3 servings, how many calories are in 1 serving
    12·1 answer
  • I need this answered
    14·1 answer
  • (Need answer quickly.) The table represents a linear function. What is the slope of the function?
    7·1 answer
  • Answer I need help plsssssssssssssss??
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!