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
baherus [9]
2 years ago
14

Solve the given differential equation by undetermined coefficients. y'' 4y = 7 sin(2x)

Mathematics
1 answer:
kherson [118]2 years ago
8 0

The solution to the given differential equation is yp=−14xcos(2x)

The characteristic equation for this differential equation is:

P(s)=s2+4

The roots of the characteristic equation are:

s=±2i

Therefore, the homogeneous solution is:

yh=c1sin(2x)+c2cos(2x)

Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:

yp=Axsin(2x)+Bxcos(2x)

If you take the second derivative of the equation above for  yp , and then substitute that result,  y′′p , along with equation for  yp  above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side,  sin(2x) , you will find:

A=0

B=−14

Therefore,

yp=−14xcos(2x)

For more information about differential equation, visit

brainly.com/question/18760518

You might be interested in
A school library has 260 DVDs in its collection. Given that 45% of the DVDs are about science and 40% or about history how many
worty [1.4K]
39 DVDs are about other subjects
7 0
3 years ago
The
Natali5045456 [20]

Answer:

Hamburger buns: 7

Hot dog buns- 4

what does it mean by system?

6 0
2 years ago
Y is inversely proportional to x and x = 10 when y = 6 what is the value of the consant? k =
Papessa [141]

Answer:

60

Step-by-step explanation:

y =  k/x ( as y is inversely proportional to x)

yx = k

--> k = yx

k = (6)(10)

k = 60

Enjoy it. I hope it will help you.

7 0
2 years ago
A student figures that he has a 4141​% chance of being let out of class late. If he leaves class​ late, there is a 3030​% chance
andreev551 [17]

Answer:

12.3%

Step-by-step explanation:

In this case, despite being different events, they are dependent on each other, therefore the final probability would be the multiplication of both probabilities.

So let L be the probability of being late that is equal to 41% and let T be the probability that the train will leave you and is equal to 30%.

That is to say:

L = 41% = 0.41

T = 30% = 0.3

So:

P = L * T

P = 0.41 * 0.3 = 0.123

So it means that the final probability is 12.3%

5 0
3 years ago
Samantha rectangular gift is 10 inches. by 12 inches and is framed with a ribbon. She wants to use the same lengths of ribbon to
vitfil [10]

Answer:

The dimension of the rectangular gift is 10 by 12 inches so let us find the perimeter of this rectangle.

Perimeter of rectangular gift = 2 (L+ W) = 2 (10 +12) = 44 inches

Since we are to use the same length of ribbon to wrap a circular clock so the perimeter or circumference of the clock should be no more than 44 inches.

2πr = 44

r = 44/2π

r = 7.003

Therefore, the maximum radius of the circular clock is 7 inches.

6 0
2 years ago
Other questions:
  • Which rational expression has a value of 0 when x = -2?
    7·1 answer
  • in a recent year the population of califorina was about 2.52x10^7 people its land area is about 4.05x10^5 km^2 what was the aver
    8·1 answer
  • A new car costs $8000 at full price. With a sales tax of 5.75%, how much will the car cost in total?​
    7·2 answers
  • A circle is centered at the point (5, -4) and passes through the point (-3, 2).
    10·2 answers
  • The diameter of a circle with endpoints A(-1,5) and B(4,-3) Use the midpoint formula to find the coordinates of the center of ci
    5·1 answer
  • Waldo has saved $14.55 in Nichols in quarters he has 21 more quarters and nickels how many quarters does Waldo have
    10·1 answer
  • Your friend comes from a large family. This list shows the ages of all of the children in her family. What is the median age of
    6·1 answer
  • Help(;ŏ﹏ŏ) plz ༎ຶ‿༎ຶ
    6·1 answer
  • If f(x) = 5x2 - 3x , what is f(-3)
    6·2 answers
  • Which equations represent an indirect variation relationship whit a constant of variation equal to -4? Select ALL correct answer
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!