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
Dafna11 [192]
3 years ago
9

Find the general solution of the given higher-order differential equation. d3u dt3 + d2u dt2 − 2u = 0

Mathematics
1 answer:
STALIN [3.7K]3 years ago
6 0

\dfrac{\mathrm d^3u}{\mathrm dt^3}+\dfrac{\mathrm d^2u}{\mathrm dt^2}-2u=0

This ODE has characteristic equation

r^3+r^2-2=(r^3-r)+(r^2+r-2)=r(r^2-1)+(r+2)(r-1)

=(r(r+1)+(r+2))(r-1)=(r^2+2r+2)(r-1)=0

which has roots at r=1,-1\pm i. Then the characteristic solution to the ODE is

u(t)=C_1e^t+C_2e^{(-1+i)t}+C_3e^{(-1-i)t}

\implies\boxed{u(t)=C_1e^t+C_2e^{-t}\cos t+C_3e^{-t}\sin t}

You might be interested in
A discount bookstore sells hardcover books for $12 and paperback books for $6. The number of hardcover books, x, sold one day wa
Thepotemich [5.8K]

Answer: the system of equations that represents this situation are

12x + 6y = 180

x = 2y

Step-by-step explanation:

Let x represent the number of hardcover books that were sold in a day.

Let y represent the number of paperback books that were sold in a day.

The discount bookstore sells hardcover books for $12 and paperback books for $6. The total sales that day were $180. It means that

12x + 6y = 180

The number of hardcover books sold that day was twice the number of paperback books. It means that

x = 2y

8 0
3 years ago
ON A RECENT MATH TEST MARY SCORED 14 OF 16 CORRECT. JOHN SCORED 23 OF 26AND JOE SCORED 9 OF 11 CORRECT. WHO ACHIEVED THE HIGHER
Andrej [43]

Answer:

I think the answer is mary

7 0
2 years ago
Read 2 more answers
How do I complete this question on arc length?
tresset_1 [31]

Answer:

v ≈ 8.5 km/h

Step-by-step explanation:

Since the diameter of the wheel is 3 m the radius will be r = 1.5 m.

Use the radius of the water wheel to find it's circumference C:

C=2\pi r                                               [set r = 1.5 m]

⇒ C=2\pi (1.5)

⇒ C=3\pi m

One revolution of the water wheel corresponds to 3\pi meters so the angular velocity 15 rmp (revolutions per minute) corresponds to:

15(3\pi ) = 45\pi m/min

Using this result, the speed of the river in kilometers per hour will be:

v=\frac{45\pi m }{1 min} ×  \frac{1 km}{1000 m} × \frac{60 min}{1 h}

⇒ v=8.48230016469  km/h

⇒ v ≈ 8.5 km/h

5 0
2 years ago
Read 2 more answers
What is the product? (3a^2b^7)(5a^3b^8)
vitfil [10]
15a^5 b^15 Is The Answer 
4 0
3 years ago
11 = x/2 - 7<br><br> Solve The equation
Novay_Z [31]

Answer: I think the Answer is 36 Let me know if i'm Right.

4 0
2 years ago
Other questions:
  • What’s the answer? A B C or D
    15·1 answer
  • PLEASE HELP !!! HURRY!! Given m || n, find x.
    14·2 answers
  • What is the midpoint of (-3, 4) and (-6, -1)
    12·1 answer
  • You have purchased a property that you intend to rent out to people. The mortgage payment is $765/month and the property taxes a
    15·1 answer
  • Spencer ran the first leg of a relay in 13.56 seconds. Michael ran the second leg. The total time it took both boys to run the r
    12·1 answer
  • Sam sees a UFO hovering in the sky. He measures the angle of elevation of the UFO at 30 0. He calls Julie, who is 15 miles close
    8·1 answer
  • Find the first five terms of the recursive sequence.<br> an= an-1 + 7 where an = 5
    13·2 answers
  • please help meeee !!!
    6·2 answers
  • A cyclist rides his bike at a rate of 18 miles per hour. What is this rate in kilometers per hour? How many kilometers will the
    5·2 answers
  • Can you please answer the question tyy
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!