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
The calculation of property tax is based on the
arlik [135]
<span>( Property Value x Assessment Rate) - Exemptions ) x Property  Tax Rate = Tax Bill I think this is the answer I'm not for sure </span>
7 0
3 years ago
I need help with this please ASAP!!!
kaheart [24]

Answer:

B and c

Step-by-step explanation:

6 0
3 years ago
The chart below shows the number of cakes Jenny bakes in each month.What is the mean number of cakes Jenny bakes in a month
Allisa [31]
(403 + 301 + 402 + 503 + 601) / 5 = 2210/5 = 442 <== ur answer
4 0
3 years ago
Read 2 more answers
6 dollars for 3 cans of tuna
SSSSS [86.1K]

Answer: 2 dollers for each can of tuna

Step-by-step explanation: 2 x 3 = 6 or 2 + 2 + 2 = 6

4 0
3 years ago
Read 2 more answers
If y = 5x − 4, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?
chubhunter [2.5K]
B is the correct answer, obtained by plugging in all the vslued
6 0
3 years ago
Read 2 more answers
Other questions:
  • Gwyneth begins solving for x in the equation 2 (x minus 4) = 5 (4 minus 2 x) + 4 x. After applying the distributive property and
    12·2 answers
  • 8x-6 greater than 18
    9·1 answer
  • Given the original amount and the percent of change, find the new amount, $25; 300%
    10·1 answer
  • The function rule for the following graph is y = 2x + 2. What is the value of y in the ordered pair (2, y)? 24 4 10 6
    6·1 answer
  • John wrote 1/5 of a paper in 1/4 of an hour how long did it take him to write an entire paper?\
    14·1 answer
  • Tony had 2/3 of a pound of strawberries. Tony let his friend Larry eat 3/8 of the strawberries. How many pounds of strawberries
    6·1 answer
  • Find the value of X or Y so that the line through the points has the given slope. (X, 0) and (4,1); slope: 1/5
    6·1 answer
  • Mercury orbits the Sun in 87 24/25 earth days. Venus orbits the Sun in 224 7/10 earth days and Mars orbits the sun in 686 49/50
    7·1 answer
  • A rectangular pyramid is sliced such that the cross section is perpendicular to its base and the cross section does not intersec
    9·2 answers
  • Determine the given rotation <br><br> please help me :( no one hasn’t helped me
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!