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
Elden [556K]
3 years ago
6

5. Find the general solution to y'''-y''+4y'-4y = 0

Mathematics
1 answer:
CaHeK987 [17]3 years ago
5 0

For any equation,

a_ny^(n)+\dots+a_1y'+a_0y=0

assume solution of a form, e^{yt}

Which leads to,

(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0

Simplify to,

e^{yt}(y^3-y^2+4y-4)=0

Then find solutions,

\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}

For non repeated real root y, we have a form of,

y_1=c_1e^t

Following up,

For two non repeated complex roots y_2\neq y_3 where,

y_2=a+bi

and,

y_3=a-bi

the general solution has a form of,

y=e^{at}(c_2\cos(bt)+c_3\sin(bt))

Or in this case,

y=e^0(c_2\cos(2t)+c_3\sin(2t))

Now we just refine and get,

\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}

Hope this helps.

r3t40

You might be interested in
find the area of the shaded regions. Give your answers as a completely simplified exact value in terms of pi. (no approximate)
Zigmanuir [339]

Answer:

Take out the area of the full circle first:

A= pi r^2

A= 3^2 x pi

A= 28.274 cm3

Area of smaller cirlces:

A= pi r^2

A= 1^2 x pi

A= 3.14159

Multiply by 2 as 2 circles: 6.28318

Substract unshaded from shaded: 28.274-6.28318

Area of shaded is 21.99082 cm3

Step-by-step explanation:

3 0
3 years ago
Sasha is outside of a building. She sees Thomas on the 4th floor at an angle of elevation (from ground level) of 48°. She then s
blagie [28]

Answer: The distance from Thomas to Sebastian is 58.39 feet

Step-by-step explanation: Please see the attachments below

6 0
3 years ago
What percent of 100 is 25? Show you work.
ANEK [815]
.25 its a quarter of 100!
4 0
3 years ago
Read 2 more answers
If there are 5 people per 10000 buses how many will there be
docker41 [41]

Answer:

45 x 5 = 225 so 225 students altogether on 5 buses

Step-by-step explanation:

have a good day

4 0
2 years ago
Read 2 more answers
Write a formula that converts weeks to days. d =
Stolb23 [73]
Days= weeks × 7
d = w × 7
7 0
3 years ago
Other questions:
  • Can someone help? ?!?!?!????!?!
    12·1 answer
  • What is the square root 5000075 cubed​
    6·1 answer
  • Need help w/ #1-8 please
    5·1 answer
  • Logx - logx - 1^2 = x - 4
    5·1 answer
  • FIND THE VALUE OF X PLEASE HELP PLEASE AND THANK U
    14·1 answer
  • What is the determinant of k=[6 8]
    10·1 answer
  • Guided Practice
    13·2 answers
  • Need help asap<br> will give brainly
    13·2 answers
  • Multiply. (−6/35)⋅14/27 What is the product? Enter your answer as a fraction, in simplified form, in the box.
    8·1 answer
  • Find the side length of the triangle.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!