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If y (x) is the solution of the differential equation  with y(1) = -1, then
  • a)
    y(x) is defined and finite in the range - ∞ < x <
  • b)
     (x) is defined and finite in the range 0 < x < 3 
  • c)
    y(x) is defined and finite in the range x >
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If y (x) is the solution of the differential equationwith y(1) = -1,th...



Now, y (1) = -1, put x = 1, y = -1


∴ for y to be defined log x must be defined i.e.. x > 0
Also when log x - 1 = 0, log x = 1 
So in the range 0 < x < 3 (option (b)). there will be a point x = 2.73 at whichy is not defined.
Also at x = e : y → ∞ (blow up).
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If y (x) is the solution of the differential equationwith y(1) = -1,thena)y(x) is defined and finite in the range - ∞ < x < 0b)(x) is defined and finite in the range 0 < x < 3c)y(x) is defined and finite in the range x > 3d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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If y (x) is the solution of the differential equationwith y(1) = -1,thena)y(x) is defined and finite in the range - ∞ < x < 0b)(x) is defined and finite in the range 0 < x < 3c)y(x) is defined and finite in the range x > 3d)None of theseCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If y (x) is the solution of the differential equationwith y(1) = -1,thena)y(x) is defined and finite in the range - ∞ < x < 0b)(x) is defined and finite in the range 0 < x < 3c)y(x) is defined and finite in the range x > 3d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y (x) is the solution of the differential equationwith y(1) = -1,thena)y(x) is defined and finite in the range - ∞ < x < 0b)(x) is defined and finite in the range 0 < x < 3c)y(x) is defined and finite in the range x > 3d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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