Sign In
Ask Question
Makena Cantrell
Mathematics
14 September, 12:14
Y''+Y'+Y=1
solve ordinary differential equation
+4
Answers (
1
)
Dwayne Bradshaw
14 September, 12:42
0
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.
Comment
Complaint
Link
Know the Answer?
Answer
Not Sure About the Answer?
Find an answer to your question 👍
“Y''+Y'+Y=1 solve ordinary differential equation ...”
in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers
You Might be Interested in
What is 19/25 in a fraction or mixed number?
Answers (2)
Solve the system by substitution. Check your solution. a-1.2b=-3 0.2b+0.6a=12
Answers (1)
Helen has 14 cats but now only 5. what is the percent decrease?
Answers (1)
Can 5, 5, and 10 be the lengths of the sides of a triangle? (yes or no answer)
Answers (2)
In a lottery game you pick ine number from 000 to 999. If you pick one such number, what is the probability that you will win the lottery
Answers (1)
New Questions in Mathematics
Tristan has 45 apples and 20 pears that he is putting into gift baskets. Each basket will have the same number of apples and pears. What is the greatest number of baskets Tristan can make with no fruit left over? Explain.
Answers (1)
85+3x-5=180 what does x equal
Answers (2)
robert wants to put lights around the edge of his deck. The deck is 43 feet long and 26 feet wide. How many yards of lights does he need?
Answers (1)
If a computer costs $600.00 and the sales tax rate is 7.5 percent, what is the total cost of the computer?
Answers (1)
What is 2/3 cup chopped nuts multiplied by 6?
Answers (2)
Home
»
Mathematics
» Y''+Y'+Y=1 solve ordinary differential equation
Sign In
Sign Up
Forgot Password?