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
timofeeve [1]
3 years ago
14

(1 point) solve the separable differential equation y′(x)=2y(x)+18−−−−−−−−−√, y′(x)=2y(x)+18, and find the particular solution s

atisfying the initial condition y(5)=9.
Mathematics
1 answer:
luda_lava [24]3 years ago
7 0
We write the equation in terms of dy/dx,
<span>y'(x)=sqrt (2y(x)+18)</span>
dy/dx = sqrt(2y + 18)
dy/dx = sqrt(2) ( sqrt(y + 9)) 

Separating the variables in the equation, we will have:
<span>1/sqrt(y + 9) dy= sqrt(2) dx </span>

Integrating both sides, we will obtain
<span>2sqrt(y+9) = x(sqrt(2)) + c </span>
<span>where c is a constant and can be determined by using the boundary condition given </span>
<span>y(5)=9 : x = 5, y = 9
</span><span>sqrt(9+9) = 5/sqrt(2) + C </span>

<span>C = sqrt(18) - 5/sqrt(2) = sqrt(2) / 2</span>

Substituting to the original equation,
sqrt(y+9) = x/sqrt(2) + sqrt(2) / 2

<span>sqrt(y+9) = (2x + 2) / 2sqrt(2) 
</span>
Squaring both sides, we will obtain,
<span>y + 9 = ((2x+2)^2) / 8</span>

y = ((2x+2)^2) / 8 - 9
You might be interested in
Translate the following expression from a numerical expression to a verbal expression: 5(2n + 7) –3
zhuklara [117]

Answer:

Five times the sum of two times a number plus seven all minus three

Step-by-step explanation:

8 0
3 years ago
Help this question question
Step2247 [10]

Answer:

-65 i suppose

Step-by-step explanation:

7 0
3 years ago
What is the value of b in the equation below? StartFraction 5 Superscript 6 Over 5 squared EndFraction = a Superscript b
Margaret [11]

Answer:

B-4

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Combine the like terms to create an equivalent -3х – 6+(-1)​
pishuonlain [190]
You can combine the -6 and -1 to -7. So the expression can be simplified as -3x-7
4 0
3 years ago
I would really appreciate some help, please!!!
shtirl [24]

Answer:

well i like corn

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • The sum of the first 6 terms of a geometric sequence is 7, 812. the common ratio is 5. what is the second term of the sequence?
    6·1 answer
  • What is the vertex of the parabola defined by the equation(x − 2)^2 = -12(y − 2)?
    6·2 answers
  • A car salesman earns 8.6% on the sale of a car priced at 24,990. What is his take home pay that day?
    9·1 answer
  • WILL GIVE BRAINLIEST !!!
    12·2 answers
  • Find the product of -5 1/3 • 4 2/5
    13·1 answer
  • Directions for constructing the centroid of a triangle? ​
    14·1 answer
  • I need help with numbers 7,8
    13·1 answer
  • Decimal form of 92/125
    14·2 answers
  • Serena uses chalk to draw a straight line on the sidewalk. The line is 12 ft long. She wants to divide the line into sections th
    15·1 answer
  • Please give me answer I will give you brilliantly​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!