GATE Exam > GATE Questions > Consider the following second-order differen...
Start Learning for Free
Consider the following second-order differential equation:
y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?
- a)-2-2t-t2
- b)-2t-t2
- c)2t-3t2
- d)-2-2t-3t2
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Consider the following second-order differential equation:y``- 4y` +3...
given y``- 4y` +3y = 2t - 3t2.
⇒ (D2 - 4D+3y = 2t - 3t2)
By the definition of particular solution-
verifying options, option (a) satisfies,
(D2-4D+3) (-2-2t - 3t2) = -2 + 8 + 8t - 6 - 6t 3t 2 = 2t - 3t2
∴(A) is constant
Most Upvoted Answer
Consider the following second-order differential equation:y``- 4y` +3...
To find the particular solution of the given second-order differential equation, we can use the method of undetermined coefficients. This method assumes that the particular solution has a similar form to the non-homogeneous term on the right-hand side of the equation.
First, let's write the given differential equation in standard form:
y'' - 4y' + 3y = 2t - 3t^2
Now, let's assume that the particular solution has the form:
y_p = At + Bt^2
Substituting this assumed form into the differential equation, we get:
y_p'' - 4y_p' + 3y_p = 2t - 3t^2
Differentiating y_p with respect to t:
y_p' = A + 2Bt
Differentiating y_p' with respect to t:
y_p'' = 2B
Now, substituting these derivatives back into the differential equation, we get:
2B - 4(A + 2Bt) + 3(At + Bt^2) = 2t - 3t^2
Simplifying the equation:
-4At + (2B + 3At) + 3Bt^2 + 2B = 2t - 3t^2
Collecting like terms:
(-4A + 2B + 3A)t + (3B)t^2 + 2B = 2t - 3t^2
Comparing coefficients, we have the following equations:
-4A + 2B + 3A = 2 (coefficient of t)
3B = -3 (coefficient of t^2)
2B = 0 (constant term)
Solving these equations, we find:
A = -2
B = 0
Therefore, the particular solution is:
y_p = -2t
Thus, the correct answer is option A: -2 - 2t - t^2.
First, let's write the given differential equation in standard form:
y'' - 4y' + 3y = 2t - 3t^2
Now, let's assume that the particular solution has the form:
y_p = At + Bt^2
Substituting this assumed form into the differential equation, we get:
y_p'' - 4y_p' + 3y_p = 2t - 3t^2
Differentiating y_p with respect to t:
y_p' = A + 2Bt
Differentiating y_p' with respect to t:
y_p'' = 2B
Now, substituting these derivatives back into the differential equation, we get:
2B - 4(A + 2Bt) + 3(At + Bt^2) = 2t - 3t^2
Simplifying the equation:
-4At + (2B + 3At) + 3Bt^2 + 2B = 2t - 3t^2
Collecting like terms:
(-4A + 2B + 3A)t + (3B)t^2 + 2B = 2t - 3t^2
Comparing coefficients, we have the following equations:
-4A + 2B + 3A = 2 (coefficient of t)
3B = -3 (coefficient of t^2)
2B = 0 (constant term)
Solving these equations, we find:
A = -2
B = 0
Therefore, the particular solution is:
y_p = -2t
Thus, the correct answer is option A: -2 - 2t - t^2.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer?
Question Description
Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer?.
Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer?.
Solutions for Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following second-order differential equation:y``- 4y` +3y = 2t - 3t2,The particular solution of the differential equations is?a)-2-2t-t2b)-2t-t2c)2t-3t2d)-2-2t-3t2Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup