Mathematics Exam > Mathematics Questions > What is the reason behind the non-existence o...
Start Learning for Free
What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?
- a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zero
- b)Because for any real function, the left-hand side of the equation becomes zero
- c)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zero
- d)Because for any real function, the left-hand side of the equation becomes infinity
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the reason behind the non-existence of any real function which...
Given: (y’)2 + 1 = 0
Consider if y = 2x, then y’ = 2 and hence the left-hand side of the equation becomes 3 which is greater than 1. Therefore, the left-hand side of the equation will always be greater than, or equal to one and thus cannot be zero and hence the differential equation is not satisfied.
Consider if y = 2x, then y’ = 2 and hence the left-hand side of the equation becomes 3 which is greater than 1. Therefore, the left-hand side of the equation will always be greater than, or equal to one and thus cannot be zero and hence the differential equation is not satisfied.
Most Upvoted Answer
What is the reason behind the non-existence of any real function which...
Given: (y’)2 + 1 = 0
Consider if y = 2x, then y’ = 2 and hence the left-hand side of the equation becomes 3 which is greater than 1. Therefore, the left-hand side of the equation will always be greater than, or equal to one and thus cannot be zero and hence the differential equation is not satisfied.
Consider if y = 2x, then y’ = 2 and hence the left-hand side of the equation becomes 3 which is greater than 1. Therefore, the left-hand side of the equation will always be greater than, or equal to one and thus cannot be zero and hence the differential equation is not satisfied.
Free Test
FREE
| Start Free Test |
Community Answer
What is the reason behind the non-existence of any real function which...
Understanding the Differential Equation
The differential equation given is (y')^2 + 1 = 0. Here, y' represents the derivative of the function y with respect to x.
Analyzing the Left-Hand Side
- The expression (y')^2 is the square of the derivative of y.
- Since squaring any real number (positive or negative) results in a non-negative value, (y')^2 is always greater than or equal to zero.
Implications of the Equation
- Adding 1 to (y')^2 means that the left-hand side, (y')^2 + 1, will always be greater than or equal to 1.
- Therefore, it cannot equal zero, as the minimum value it can take is 1.
Conclusion on Existence of Real Functions
- Since (y')^2 + 1 = 0 implies that the left-hand side equals zero, which contradicts the earlier conclusion that it is always at least 1, there cannot exist any real function y(x) that satisfies this differential equation.
Final Answer
Thus, the reason behind the non-existence of any real function satisfying the differential equation is:
- The left-hand side will always be greater than or equal to one and thus cannot be zero (Option C).
The differential equation given is (y')^2 + 1 = 0. Here, y' represents the derivative of the function y with respect to x.
Analyzing the Left-Hand Side
- The expression (y')^2 is the square of the derivative of y.
- Since squaring any real number (positive or negative) results in a non-negative value, (y')^2 is always greater than or equal to zero.
Implications of the Equation
- Adding 1 to (y')^2 means that the left-hand side, (y')^2 + 1, will always be greater than or equal to 1.
- Therefore, it cannot equal zero, as the minimum value it can take is 1.
Conclusion on Existence of Real Functions
- Since (y')^2 + 1 = 0 implies that the left-hand side equals zero, which contradicts the earlier conclusion that it is always at least 1, there cannot exist any real function y(x) that satisfies this differential equation.
Final Answer
Thus, the reason behind the non-existence of any real function satisfying the differential equation is:
- The left-hand side will always be greater than or equal to one and thus cannot be zero (Option C).
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
Question Description
What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. 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 What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. Can you explain this answer?.
What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. 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 What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. Can you explain this answer?.
Solutions for What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. 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 What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0?a)Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zerob)Because for any real function, the left-hand side of the equation becomes zeroc)Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zerod)Because for any real function, the left-hand side of the equation becomes infinityCorrect answer is option 'C'. 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 on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily