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
makkiz [27]
3 years ago
9

Show that y=2e^(−x) cos(x)−e^(−x) sin(x) is a solution to y''+2y'+2y=0.

Mathematics
2 answers:
Temka [501]3 years ago
5 0

Answer:

y=2e^(−x)cosx−e^(−x)sinx

y = e^(-x)[2cosx - sinx]

y': product law

y' = -e^(-x)[2cosx - sinx] + e^(-x)[-2sinx - cosx]

y' = -e^(-x)[2cosx - sinx + 2sinx + cosx]

y' = -e^(-x)[3cosx + sinx]

y" = e^(-x)[3cosx + sinx] - e^(-x)[-3sinx + cosx]

y" = e^(-x)[3cosx - cosx + sinx + 3sinx]

y" = e^(-x)[2cosx + 4sinx]

y" + 2y' + 2y

e^(-x)[2cosx + 4sinx] - 2e^(-x)[3cosx + sinx] +2e^(-x)[2cosx - sinx]

e^(-x)[4sinx - 2sinx - 2sinx + 2cosx - 6 cosx + 4cosx]

= e^(-x) × 0

= 0

Hence a solution

lara31 [8.8K]3 years ago
4 0

Answer:

see below

Step-by-step explanation:

y' = -2e⁻ˣcos(x) -sin(x)2e⁻ˣ +e⁻ˣsin(x)-cos(x)e⁻ˣ = e⁻ˣ(-2cos(x)-2sin(x)+sin(x) -cos(x))

=e⁻ˣ(-3cos(x)-sin(x))

y'' = -e⁻ˣ(-3cos(x)-sin(x)) + (3sin(x)-cos(x))e⁻ˣ

y'' = e⁻ˣ[3cos(x)+sin(x) + 3sin(x)-cos(x)] = e⁻ˣ[2cos(x)+4sin(x)]

y''+2y'+2y = 0

e⁻ˣ[2cos(x)+4sin(x)] + 2[e⁻ˣ(-3cosx-sinx)] + 2[2e⁻ˣ cos(x)−e⁻ˣ sin(x)]

e⁻ˣ[2cos(x)+4sin(x)-6cos(x)-2sin(x)+4cos(x)-2sin(x)]

e⁻ˣ[-4cos(x)+2sin(x)+4cos(x)-2sin(x)]

e⁻ˣ[0cos(x)+0sin(x)] = 0

You might be interested in
What is 11/12 – 3/8 <br> A) 2 <br> B) 1/2 <br> C) 13/24 <br> D) 21/32
Pepsi [2]

Hey! Answer to this would be 13/24.

4 0
3 years ago
Read 2 more answers
15 cm<br> 4 cm<br> cm<br> V=____cm3
bonufazy [111]

Answer:

V=(πr^2 x h)/3

lets use π as 3.14 cause I dont know what pi u using

3.14 x 4^2 x 15 = 753.6/3 = 251.2

If you're using π as your pi, than just replace 3.14 by π on calculator

Hope that answers your question

8 0
3 years ago
5,345,238. How are the two 3 related
Lemur [1.5K]
Each just has different amounts of 0s
5 0
3 years ago
Read 2 more answers
I really need this answer to be correct
Fed [463]
It is unchanged because the same number would still be in the middle and there would still be the same amount of numbers

if
11,15,21,22,23,27,30 before 22 is the median

if
11,15,21,22,23,27,30 after 22 is still the median

The median is unchanged
4 0
3 years ago
BRAINLIST OPPORTUNITY<br><br> what is the slope of the line on the graph?
Vika [28.1K]

Answer:

2,4

Step-by-step explanation:

go up by 8 then right 16

4 0
3 years ago
Read 2 more answers
Other questions:
  • In a certain region each person is understood to live either in the city or the suburbs. Each year 6% of the city population mov
    13·1 answer
  • Which rate of change is bigger 1/4 or 3/4
    14·2 answers
  • There are 750 student at a school If each Classroom hold 30 and student how many classrooms are needed at th
    14·2 answers
  • Solve the formula F=9/5C+32 for degrees<br> Celcuis C. show all your steps
    14·1 answer
  • The diameter of tammys miniature pie is 6.5 cm.Based on this measurement what would the circumference of her pie be
    6·1 answer
  • Estimate the sum 4.86+9.57​
    15·2 answers
  • Question is in photo
    10·1 answer
  • Find the slope: (-2, -5), (7, 8)
    7·2 answers
  • PLEASE SOLVE THIS FAST 6x=10x+4
    5·2 answers
  • In a survey of 2264 adults, 729 say they believe in ufos. construct a 95 confidence interval for the population proportion of ad
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!