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
Rudik [331]
3 years ago
13

A particular solution of the differential equation y"- 2y' + y = cosx is:

Mathematics
1 answer:
Elden [556K]3 years ago
5 0

Answer:

 y_p = - sin(x) / 2

Step-by-step explanation:

Given:

- The following ODE as such:

                                  y" - 2y' + y = cos(x)

Find:

The particular solution.

Solution:

- The particular solution resembles the non-homogeneous part of the ODE.

- So lets suppose we have a solution:

                                 y_p = A*cos(x) + B*sin(x)

Where, A is constant that needs to be determined.

- Differentiate the particular solution 2 times:

                                y'_p = - A*sin(x) + B*cos(x)

                                y"_p = -A*cos(x) - B*sin(x)

- Use the derivatives and plug the back in the ODE as follows:

   -A*cos(x) - B*sin(x) + 2*(A*sin(x) - B*cos(x)) + A*cos(x) + B*sin(x) = cos(x)

- Simplify and compare coefficients:

                               2A*sin(x)  - 2B*cos(x) = cos(x)  

We have:                 2A = 0     ,   -2B = 1

Hence,                     A = 0      ,   B = -1/2

- Hence we can write our particular solution to be:

                              y_p = - sin(x) / 2    .....   Hence option C            

You might be interested in
If asphalt pavement costs $0.70 per square foot, find the cost to pave the circular How much does it cost to pave this road?
Hunter-Best [27]

Answer:

Cost to pave the road = $4257

Step-by-step explanation:

Area of the pavement = Area of the outer circle - Area of the internal circle

Area of the outer circle = πr²

                                       = π(55)²

                                       = 3025π square feet

Area of the inner circle = π(33)²

                                       = 1089π square feet

Area of the pavement = 3025π - 1089π

                                     = 1936π

                                     = 6082.12 square feet

Cost of pavement = $0.70 per square feet

Therefore, cost of 6082.12 square feet = 6082.12 × 0.70

                                                                 = 4257.49

                                                                 ≈ $4257

Cost to pave the road = $4257                                    

5 0
2 years ago
Pls help I need a good grade
aleksley [76]

Answer:

f= -14

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Find Missing Angle
Neporo4naja [7]

Answer:

75 degrees

Step-by-step explanation:

Use trigonometry

we are given opposite(27) and hypotenuse(28), so use sin

sin=opp/hyp

sin(x)=27/28

x=arcsin(27/28)

x=74.64111442

6 0
3 years ago
Can someone and give me the right answer
kolezko [41]

The 1st option is your answer,

because to solve c, the -11 and 11 = 0, so your left with adding 23 and 11, then you divide -4 on both sides to get the variable (x) by itself

And for f, you only need to divide -4 on both sides to get x by itself.

6 0
3 years ago
Conditions of a triangle = AAA
34kurt

Answer:

One triangle

Step-by-step explanation:

That's the answer....

3 0
2 years ago
Other questions:
  • Been 3 hours with no answer.
    15·1 answer
  • If you answered 18 questions correct on a 30 question test, what is your score?
    5·1 answer
  • Rashad filled the bottom layer of a toy box with 15 wooden blocks he stacked 2 more wooden blocks on top of the bottom layer wha
    13·2 answers
  • What is the square root of -1​
    14·2 answers
  • From the set {6, 16, 24}, use substitution to determine which value of x makes the inequality true. 4 + x < 20 A. 16 B. 6 C.
    13·1 answer
  • A project has an initial cost of $40,000, expected net cash inflows of $10,000 per year for 8 years, and a cost of capital of 14
    11·1 answer
  • Please help giving 50 points and brainlyest if correct
    5·2 answers
  • The graph of a linear function passes through the points (7,0) and (-8, 45). A
    10·1 answer
  • Please select the best answer from the choices provided<br>A<br>B<br>C<br>D​
    14·1 answer
  • Label the vertices and all the elements needed. find x
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!