UPSC Exam > UPSC Questions > Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?...
Start Learning for Free
Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?
a)it has unique solution
b)no solution
c) solution exist but not uniquely
d) none of these?
a)it has unique solution
b)no solution
c) solution exist but not uniquely
d) none of these?
Most Upvoted Answer
Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution ...
Analysis of the Differential Equation
- The given differential equation is Y' = 2√y.
- It is a first-order ordinary differential equation.
Initial Condition
- The initial condition given is y=0, x=0.
- This means that at x=0, the value of y is 0.
Existence and Uniqueness of Solution
- The given differential equation is Y' = 2√y.
- It can be rewritten as dy/dx = 2√y.
- By separating variables and integrating, we get 1/√y dy = 2dx.
- Integrating both sides gives 2√y = 2x + C, where C is the constant of integration.
- Substituting the initial condition y=0, x=0 into the equation gives 0 = 0 + C, which implies C=0.
- Therefore, the solution to the differential equation is √y = x.
- Squaring both sides gives y = x^2.
Conclusion
- The solution to the given differential equation with the initial condition y=0, x=0 is y=x^2.
- This solution exists and is unique in the neighborhood of x=0.
- Therefore, the correct option is a) it has a unique solution.
- The given differential equation is Y' = 2√y.
- It is a first-order ordinary differential equation.
Initial Condition
- The initial condition given is y=0, x=0.
- This means that at x=0, the value of y is 0.
Existence and Uniqueness of Solution
- The given differential equation is Y' = 2√y.
- It can be rewritten as dy/dx = 2√y.
- By separating variables and integrating, we get 1/√y dy = 2dx.
- Integrating both sides gives 2√y = 2x + C, where C is the constant of integration.
- Substituting the initial condition y=0, x=0 into the equation gives 0 = 0 + C, which implies C=0.
- Therefore, the solution to the differential equation is √y = x.
- Squaring both sides gives y = x^2.
Conclusion
- The solution to the given differential equation with the initial condition y=0, x=0 is y=x^2.
- This solution exists and is unique in the neighborhood of x=0.
- Therefore, the correct option is a) it has a unique solution.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these?
Question Description
Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these?.
Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these?.
Solutions for Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these? defined & explained in the simplest way possible. Besides giving the explanation of
Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these?, a detailed solution for Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these? has been provided alongside types of Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these? theory, EduRev gives you an
ample number of questions to practice Y'=2✓y ,y=0,x=0 which is correct in nbd of 0?a)it has unique solution b)no solution c) solution exist but not uniquely d) none of these? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
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