Mathematics Exam > Mathematics Questions > The particular integral of the differential e...
Start Learning for Free
The particular integral of the differential equation
y" + y' + 3y = 5 cos(2x + 3) is
y" + y' + 3y = 5 cos(2x + 3) is
- a)2 cos(2x + 3) - sin (2x + 3)
- b)2 sin (2x + 3) + cos(2x + 3)
- c)sin (2x + 3) - 2 cos (2x + 3)
- d)2 sin (2x + 3) - cos (2x + 3)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The particular integral of the differential equationy" + y' +...
we have (D2 + D + 3)y = 5 cos(2x + 3)
So,
So,
Free Test
FREE
| Start Free Test |
Community Answer
The particular integral of the differential equationy" + y' +...
In order to find the particular integral of a differential equation, we first need to determine the homogeneous solution. The homogeneous solution is the solution to the differential equation when the right-hand side is set to zero.
Once we have the homogeneous solution, we can then find a particular solution that satisfies the original differential equation. This particular solution is typically found by making an educated guess based on the form of the differential equation.
For example, if the differential equation is of the form:
y'' + ay' + by = f(x)
where a and b are constants, we can guess that the particular solution has a similar form to f(x). We then substitute this guess into the differential equation and solve for the unknown coefficients.
The particular integral is the sum of the homogeneous solution and the particular solution.
It's important to note that the method for finding the particular integral can vary depending on the specific form of the differential equation. There are different techniques for different types of equations, such as linear, homogeneous, and non-homogeneous equations.
Once we have the homogeneous solution, we can then find a particular solution that satisfies the original differential equation. This particular solution is typically found by making an educated guess based on the form of the differential equation.
For example, if the differential equation is of the form:
y'' + ay' + by = f(x)
where a and b are constants, we can guess that the particular solution has a similar form to f(x). We then substitute this guess into the differential equation and solve for the unknown coefficients.
The particular integral is the sum of the homogeneous solution and the particular solution.
It's important to note that the method for finding the particular integral can vary depending on the specific form of the differential equation. There are different techniques for different types of equations, such as linear, homogeneous, and non-homogeneous equations.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
Question Description
The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer?.
The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer?.
Solutions for The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The particular integral of the differential equationy" + y' + 3y = 5 cos(2x + 3) isa)2 cos(2x + 3) - sin (2x + 3)b)2 sin (2x + 3) + cos(2x + 3)c)sin (2x + 3) - 2 cos (2x + 3)d)2 sin (2x + 3) - cos (2x + 3)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup