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
Elodia [21]
3 years ago
10

Find the solution to the initial value problem

Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
3 0

Answer:

y = (11x + 13)e^(-4x-4)

Step-by-step explanation:

Given y'' + 8y' + 16 = 0

The auxiliary equation to the differential equation is:

m² + 8m + 16 = 0

Factorizing this, we have

(m + 4)² = 0

m = -4 twice

The complimentary solution is

y_c = (C1 + C2x)e^(-4x)

Using the initial conditions

y(-1) = 2

2 = (C1 -C2) e^4

C1 - C2 = 2e^(-4).................................(1)

y'(-1) = 3

y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)

3 = -4(C1 - C2)e^4 + C2e^4

-4C1 + 5C2 = 3e^(-4)..............................(2)

Solving (1) and (2) simultaneously, we have

From (1)

C1 = 2e^(-4) + C2

Using this in (2)

-4[2e^(-4) + C2] + 5C2 = 3e^(-4)

C2 = 11e^(-4)

C1 = 2e^(-4) + 11e^(-4)

= 13e^(-4)

The general solution is now

y = [13e^(-4) + 11xe^(-4)]e^(-4x)

= (11x + 13)e^(-4x-4)

You might be interested in
How do you find the original price after a discount. The sales price is 55.50 and the percent of discount is 75%.
Arte-miy333 [17]
Well first we know that 55.50 is 25% so I guess multiply it by 3 to get the full price equalling nearly 166 which is closest to 165, so that’d be my answer. Sorry if wrong.
6 0
2 years ago
Read 2 more answers
1.73639 rounded to the nearest thousanth
Maurinko [17]
^ is in the thousadths place so look for the number before it, which is 3. 3 is less than 5 so 6 stays as is so it becomes 1.736
8 0
3 years ago
* PLEASE HELP *
LiRa [457]
The first one is 135 per hour if you barely went 90 miles in a hour in a half, and the second one it is 1/3+1/3+1/3 you add 2 more thirds so it means you add 2 forths 1/4/+1/4+1/4=3/4 so you paint 3/4's of the wall
5 0
3 years ago
Are the equations 3x - -9 and 4x - -12 equivalent? Explain.<br> Please Help!!
konstantin123 [22]
No because  when  you do 3*--9 = 27 and 4*--12 =48

7 0
3 years ago
As an estimation we are told £3 is 4 euro.Convert £13.50 to euros
bixtya [17]

Answer:

15.07 Euro

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • I need help desperately a,b and c
    15·1 answer
  • Plz help dont get it
    6·2 answers
  • Use the remainder theorem to determine the remainder when 5w3 − 2w + 10 is divided by w + 3.
    13·1 answer
  • Cyndee is taking her siblings out for dessert. Ice cream, c, costs $4.00 per cone. Brownies, b, are $2.00 each. Water for everyo
    6·1 answer
  • Which fraction below represents a repeating decimal?
    6·1 answer
  • What is the area of this triangle?
    6·1 answer
  • Find the common difference of the arithmetic sequence.
    15·2 answers
  • millicent earned $435 last year in interest. If $3000 was invested at a certain rate of return and $4500 was invested in a fund
    10·1 answer
  • Is 5/12 closer to 0, 1, 1/2
    5·2 answers
  • 35. Cindy walks at a constant rate of 2 miles per hour. She leaves home to walk to her friend Jenny's house at 9 am. When she is
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!