Sign In
Ask Question
Kristian Dudley
Mathematics
11 January, 08:24
Find the general solution of y"-4y'-5y=sin4t
+3
Answers (
2
)
Lorelai Ross
11 January, 08:37
0
y = - 21/697 sin (4t) + 16/697 cos (4t) + C₁e^ (-t) + C₂e^ (5t)
Step-by-step explanation:
y" - 4y' - 5y = sin (4t)
This is a second-order, non-homogeneous equation with constant coefficients. The general solution is the sum of the complementary and particular solutions.
First, find the complementary solution:
y" - 4y' - 5y = 0
s² - 4s - 5 = 0
(s - 5) (s + 1) = 0
s = - 1 or 5
y = C₁e^ (-t) + C₂e^ (5t)
Next, find the particular solution. Since g (t) = sin (4t):
y = A sin (4t) + B cos (4t)
y' = 4A cos (4t) - 4B sin (4t)
y" = - 16A sin (4t) - 16B cos (4t)
Substituting:
y" - 4y' - 5y = sin (4t)
-16A sin (4t) - 16B cos (4t) - 4 (4A cos (4t) - 4B sin (4t)) - 5 (A sin (4t) + B cos (4t)) = sin (4t)
-16A sin (4t) - 16B cos (4t) - 16A cos (4t) + 16B sin (4t) - 5A sin (4t) - 5B cos (4t) = sin (4t)
(16B - 21A) sin (4t) - (16A + 21B) cos (4t) = sin (4t)
Match the coefficients:
16B - 21A = 1, 16A + 21B = 0
Solve the system of equations:
A = - 21/16 B
16B - 21 (-21/16 B) = 1
16B + 441/16 B = 1
697B/16 = 1
B = 16/697
A = - 21/697
Therefore, the general solution is:
y = - 21/697 sin (4t) + 16/697 cos (4t) + C₁e^ (-t) + C₂e^ (5t)
Comment
Complaint
Link
Boston Miranda
11 January, 08:47
0
therebisnt an answer
Comment
Complaint
Link
Know the Answer?
Answer
Not Sure About the Answer?
Find an answer to your question 👍
“Find the general solution of y"-4y'-5y=sin4t ...”
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 numbers complete the sentence? 5 + 6 =, therefore 11 - 6 =
Answers (1)
Sports jacket cost 100 dollars at 30 percent off what is the amount of discount
Answers (2)
63=.5 (x+3) (2x+10) it is solving for x. The entire problem revolves around a triangle. 63 is the square unit area of the triangle.
Answers (2)
Each hour, the temperature rose by 1 and 1/2 degrees. What was the change in temperature in 1 and 1/2 hours? A. 1 1/4. B. 2 3/4 C. 2 1/4. D. 3
Answers (1)
How to get to standard form from slope intercept?
Answers (1)
New Questions in Mathematics
Jillian is trying to save water so she reuces the size of her square grass lawn by 8 ft on each side the area of the smaller lawn is 144 square feet in the equation (x-2) ^2=144 x represents the side measure of the original lawn.
Answers (1)
True or False: The angle measure for sin = 2/25 is 4.59 Degrees
Answers (1)
Owino gets paid 280 per week plus 5% commission on all sales for selling electronic
Answers (1)
Is 53 divided by 7 compatible
Answers (1)
Luis is finding 9-6+2. Find his mistake and correct it : 9-8 = 1
Answers (2)
Home
»
Mathematics
» Find the general solution of y"-4y'-5y=sin4t
Sign In
Sign Up
Forgot Password?