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
fiasKO [112]
3 years ago
15

Y" +2y' +17y=0; y(0)=3, y'(0)=17

Mathematics
1 answer:
Ronch [10]3 years ago
8 0

Answer:

The solution is y(t)=e^{-t}(\cos 32t + (\frac{5}{8}) \sin 32t)

Step-by-step explanation:

We need to find the solution of y''+2y'+17y=0 with

condition y(0)=3,\ y'(0)=17

This is a homogeneous equation with characteristic polynomial

r^{2}+2r+17=0

using quadratic formula x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}

r=\frac{-2\pm \sqrt{2^{2}-4(1)(17)}}{2(1)}

r=\frac{-2\pm \sqrt{4-68}}{2}

r=\frac{-2\pm \sqrt{-64}}{2}

r=\frac{-2\pm 64i}{2}

r=-1 \pm 32i

The general solution for eigen value a \pm ib is

y(t)=e^{at}(A \cos bt + B \sin bt)

y(t)=e^{-t}(A \cos 32t + B \sin 32t)

Differentiate above with respect to 't'

y'(t)=-e^{-t}(A \cos 32t + B \sin 32t) + e^{-t}(-32A \sin 32t + 32B \cos 32t)

Since, y(0)=3

y(0)=e^{0}(A \cos(0) + B \sin(0))

3=(A \cos(0) +0)

so, A=1

Since, y'(0)=17

y'(0)=-e^{0}(3 \cos(0) + B \sin(0)) + e^{0}(-32(3) \sin(0) + 32B \cos (0))

17=-(3 \cos(0)) + (0 + 32B \cos (0))

17=-3 + 32B

add both the sides by 3,

17+3 = 32B

20= 32B

divide both the sides, by 32,

\frac{20}{32}= B

\frac{5}{8}= B

Put the value of constants in y(t)=e^{-t}(A \cos 32t + B \sin 32t)

y(t)=e^{-t}((1) \cos 32t + (\frac{5}{8}) \sin 32t)

Therefore, the solution is y(t)=e^{-t}(\cos 32t + (\frac{5}{8}) \sin 32t)

You might be interested in
Higher Order Thinking Greg has a bag
velikii [3]

Answer:

shes less likely to pick blue from the second bag

Step-by-step explanation:

first you divide 10 by 25 which will give you 40 percent

then

you divide 75 by 250 which will give you 30 percent

which makes it less likely for Greg to pick blue from the second bag

8 0
2 years ago
Functions.
never [62]

Answer:

2,5 and 6

Step-by-step explanation:

The answer is going to be option 2, 5 and 6 because the line touches -4,2 and 4 on the x axis. And these are the x values so that's why this is going to be the answer.

Hope this information helps you!

4 0
3 years ago
 The volume of a cylinder is
Dima020 [189]

The volume of a cylinder is equal to \frac{1}{3}\pi  r^{2} h, where r is the radius of the cylinder and h is its height.

324 =  \frac{1}{3}\pi  r^{2} h

324 = \frac{1}{3} x 3.14 x r^{2} x 1

309.55 = r^{2}

r = \sqrt{309.55}

r = approx. 17.59 inches

I hope this answer helped you! If you have any questions, feel free to ask away.

7 0
3 years ago
Nancy found that x=1 is one solution to the quadratic equation (x 2)2=a. what is the value of a?
trasher [3.6K]

The value of the a in the quadratic equation is 4.

According to the statement

we have given that the x = 1 and the given equation is  (2x)^2=a

And we have to find the value of A here.

So, For this purpose, we know that the

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

And the given quadratic equation is

(2x)^2 = a

we know that the x  = 1 and put the value of x in it then

(2(1))^2= a

(2)^2= a

a  = 4.

Now for rechecking of the value, put a = 4 in the given equation then

(2x)^2 = a

Put a  = 4

Then

(2x)^2 = 4

2x = 2

And the value of x become

x = 1.

Which equal to the given value of the x which is 1.

So, The value of the a in the quadratic equation is 4.

Learn more about Quadratic equation here

brainly.com/question/1214333

#SPJ4

7 0
2 years ago
16,048 divided by 1/16​
natima [27]

Answer:256768

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Simplify jk ∙ 6 ∙ 3.<br><br> 6jk + 3<br> 18jk<br> 18jkl
    11·1 answer
  • A fee of 12.50 is deducted each month from Aubryn's bank account. She currently has a balance of $75.00 in her account. She must
    12·1 answer
  • You claim to have a magic coin that will land on heads whenever you want. Your friend dares you to prove it by tossing 4 heads i
    6·2 answers
  • Three randomly chosen people decide to check the calendar from the year they were born to see what day of the week they were bor
    15·1 answer
  • -4/9 + (-1/3) ? Helppppp
    8·1 answer
  • PLEASE HELP ASAP
    6·2 answers
  • Help with math pls thanks so much
    11·2 answers
  • PLease Help! I will give you the brainiest and a lot of points!
    12·1 answer
  • Troy and Lisa were shopping for school supplies. Troy bought 3 notebooks and 5 thumb drives for $20.25. Lisa bought 8 notebooks
    8·1 answer
  • PLZzzz helllpppp!!!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!