Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > The solution of differential equation dy = (1...
Start Learning for Free
The solution of differential equation dy = (1-y) dx is
- a)y = e-x c
- b)y = ex c
- c)y = 1 ce-x
- d)y = 1 cex
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y...
dy = (1 – y) dx
y = 1 ce-x
Most Upvoted Answer
The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y...
Understanding the Differential Equation
The given differential equation is:
dy = (1 - y) dx
This means we can rearrange it to find the relationship between y and x.
Rearranging the Equation
We can rewrite the equation as:
dy / (1 - y) = dx
This format allows us to separate variables, making it easier to integrate both sides.
Integrating Both Sides
Now, integrate both sides:
∫ dy / (1 - y) = ∫ dx
The left side integrates to -ln|1 - y|, and the right side integrates to x + C, where C is the integration constant. Thus, we have:
-ln|1 - y| = x + C
Solving for y
To solve for y, we exponentiate both sides:
|1 - y| = e^(-x - C)
This simplifies to:
1 - y = ±e^(-x - C)
Now isolate y:
y = 1 - ±e^(-x - C)
By setting a new constant K = ±e^(-C), we can express y as:
y = 1 - Ke^(-x)
Analyzing the Solutions
The form y = 1 - Ke^(-x) indicates that as x approaches infinity, y approaches 1 (the horizontal asymptote). Therefore, the solution of this differential equation approaches the line y = 1.
Conclusion
Thus, the correct answer is indeed option 'C', which indicates that the solution converges to the constant value:
y = 1.
The given differential equation is:
dy = (1 - y) dx
This means we can rearrange it to find the relationship between y and x.
Rearranging the Equation
We can rewrite the equation as:
dy / (1 - y) = dx
This format allows us to separate variables, making it easier to integrate both sides.
Integrating Both Sides
Now, integrate both sides:
∫ dy / (1 - y) = ∫ dx
The left side integrates to -ln|1 - y|, and the right side integrates to x + C, where C is the integration constant. Thus, we have:
-ln|1 - y| = x + C
Solving for y
To solve for y, we exponentiate both sides:
|1 - y| = e^(-x - C)
This simplifies to:
1 - y = ±e^(-x - C)
Now isolate y:
y = 1 - ±e^(-x - C)
By setting a new constant K = ±e^(-C), we can express y as:
y = 1 - Ke^(-x)
Analyzing the Solutions
The form y = 1 - Ke^(-x) indicates that as x approaches infinity, y approaches 1 (the horizontal asymptote). Therefore, the solution of this differential equation approaches the line y = 1.
Conclusion
Thus, the correct answer is indeed option 'C', which indicates that the solution converges to the constant value:
y = 1.
Free Test
FREE
| Start Free Test |
Community Answer
The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y...
dy = (1 – y) dx
y = 1 ce-x
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Similar Electronics and Communication Engineering (ECE) Doubts
Top Courses for Electronics and Communication Engineering (ECE)View all
The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer?
Question Description
The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer?.
The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free.
Here you can find the meaning of The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The solution of differential equation dy = (1-y) dx isa)y = e-x cb)y = ex cc)y = 1 ce-xd)y = 1 cexCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
|
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
x
![]()
Best way to Prepare for Electronics and Communication Engineering (ECE)
Learn | Test | Discuss | Repeat
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup