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
Archy [21]
3 years ago
7

Y''+Y'+Y=1 solve ordinary differential equation

Mathematics
1 answer:
taurus [48]3 years ago
5 0

Answer:

y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1

Step-by-step explanation:

y" + y' + y = 1

This is a second order nonhomogenous differential equation with constant coefficients.

First, find the roots of the complementary solution.

y" + y' + y = 0

r² + r + 1 = 0

r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)

r = [ -1 ± √(1 − 4) ] / 2

r = -1/2 ± i√3/2

These roots are complex, so the complementary solution is:

y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)

Next, assume the particular solution has the form of the right hand side of the differential equation.  In this case, a constant.

y = c

Plug this into the differential equation and use undetermined coefficients to solve:

y" + y' + y = 1

0 + 0 + c = 1

c = 1

So the total solution is:

y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1

To solve for c₁ and c₂, you need to be given initial conditions.

You might be interested in
#18-4: Douglas invests $550 in high-yield savings account. The account pays 2.1% simple interest annually. If he doesn't add or
kap26 [50]

Answer:

No

Step-by-step explanation:

You want to calculate the interest on $550 at 2.1% interest per year after 4 years.

The formula we'll use for this is the simple interest formula, or:

I = P x r x t

P is the principal amount, $550.00.

r is the interest rate, 2.1% per year, or in decimal form, 2.1/100=0.021.

t is the time involved, 4 years.

So, t is 4 year time periods.

To find the simple interest, we multiply 550 × 0.021 × 4 to get that:

The interest is: $46.20

3 0
3 years ago
A diameter is a line segment whose endpoints are on a circle. It is a special type of chord because it must contain the _____ of
Oksana_A [137]

Answer:

Center

Step-by-step explanation:

A diameter is a line segment whose endpoints are on a circle. It is a special type of chord because it must contain the center of the circle.

7 0
3 years ago
1/2(4x−5)+52=10
Sav [38]
In the first one the options they give you are wrong, in fact you can prove it yourself, none of the options will give you as a result 10
I hope I helped you out
greetings!

7 0
3 years ago
What’s the answer to this?<br> I have no idea how to do it
Nimfa-mama [501]

Answer:

0

Step-by-step explanation:

f(x) = y

To find f(2), it means to find the value of y when x = 2.

From the graph, when x = 2, the corresponding y-coordinate = 0.

Therefore,

f(2) = 0

5 0
3 years ago
What's the answer for this? ​
grin007 [14]

Answer:

A

Step-by-step explanation:

Observe the coordinates of C, it's (5,2). Now observe C' which is (2, - 5). Hence the rule is (x, y) -> (y, - x)

3 0
3 years ago
Other questions:
  • The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they
    6·1 answer
  • Solve the answer y=6x−8<br> Thanks for helping
    6·1 answer
  • If a coin is flipped 4 times what is the probability that a coin will land on heads 4 times
    7·1 answer
  • Find the unit rate ( miles per gallon ): 50 miles on 2 1/2 gallons.
    10·2 answers
  • . If the length of the side of a table is 3 more than twice its width, what is the expression
    5·1 answer
  • What is it in fraction form?
    8·2 answers
  • I need help
    12·2 answers
  • EB bisects ∠RED. Find the measure of ∠BED if ∠REB = 5x – 3 and ∠RED = 8x + 16
    7·1 answer
  • If R(x) and S(x) are inverse functions, which statement must be true?
    15·1 answer
  • Which polygon has an interior<br> angle sum of 1260°?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!