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If φ(x, y) = 0 is a singular solution, then φ(x, y) is a factor of
- a)p-discriminant only
- b)c-discriminant only
- c)Both p and c-discriminant
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If φ(x, y) = 0 is a singular solution, then φ(x, y) is a facto...
Explanation:
Singular Solution:
A singular solution to a differential equation is a solution that satisfies the equation but not its derivatives. In other words, if φ(x, y) = 0 is a singular solution, then φ(x, y) is a factor of the differential equation.
Factor of p-discriminant:
The p-discriminant is a factor that appears in the characteristic equation of a linear differential equation. If φ(x, y) = 0 is a singular solution, it implies that the differential equation has a repeated root in its characteristic equation. Therefore, φ(x, y) is a factor of the p-discriminant.
Factor of c-discriminant:
The c-discriminant is a factor that appears in the characteristic equation of a nonlinear differential equation. If φ(x, y) = 0 is a singular solution, it implies that the differential equation has a multiple root in its characteristic equation. Therefore, φ(x, y) is a factor of the c-discriminant.
Conclusion:
Since a singular solution is a factor of both the p-discriminant and the c-discriminant, the correct answer is option 'C'.
Singular Solution:
A singular solution to a differential equation is a solution that satisfies the equation but not its derivatives. In other words, if φ(x, y) = 0 is a singular solution, then φ(x, y) is a factor of the differential equation.
Factor of p-discriminant:
The p-discriminant is a factor that appears in the characteristic equation of a linear differential equation. If φ(x, y) = 0 is a singular solution, it implies that the differential equation has a repeated root in its characteristic equation. Therefore, φ(x, y) is a factor of the p-discriminant.
Factor of c-discriminant:
The c-discriminant is a factor that appears in the characteristic equation of a nonlinear differential equation. If φ(x, y) = 0 is a singular solution, it implies that the differential equation has a multiple root in its characteristic equation. Therefore, φ(x, y) is a factor of the c-discriminant.
Conclusion:
Since a singular solution is a factor of both the p-discriminant and the c-discriminant, the correct answer is option 'C'.
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If φ(x, y) = 0 is a singular solution, then φ(x, y) is a factor ofa)p-discriminant onlyb)c-discriminant onlyc)Both p and c-discriminantd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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If φ(x, y) = 0 is a singular solution, then φ(x, y) is a factor ofa)p-discriminant onlyb)c-discriminant onlyc)Both p and c-discriminantd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If φ(x, y) = 0 is a singular solution, then φ(x, y) is a factor ofa)p-discriminant onlyb)c-discriminant onlyc)Both p and c-discriminantd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If φ(x, y) = 0 is a singular solution, then φ(x, y) is a factor ofa)p-discriminant onlyb)c-discriminant onlyc)Both p and c-discriminantd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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