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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.
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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?
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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?.
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