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Differential equation |y'| + |y| = 0 has
- a)GS solution
- b)GS solution but no arbitrary constant
- c)particular solution which is bounded
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Differential equation |y| + |y| = 0 hasa)GS solutionb)GS solution but ...
Explanation:
To solve the given differential equation |y| |y| = 0, we can break it down into two separate cases:
Case 1: y ≥ 0
In this case, the equation becomes y^2 = 0, which implies that y = 0 is the only solution.
Case 2: y < />
In this case, the equation becomes -y^2 = 0, which is not possible as the square of a negative number is always positive. Therefore, there are no solutions in this case.
Since the differential equation has different solutions for different cases, it does not have a general solution (option a) or a general solution with arbitrary constants (option b).
However, it is worth noting that the equation does have a particular solution y = 0, which satisfies the equation for both cases. This particular solution is bounded since it remains at zero for all values of x. Therefore, the correct answer is option c) particular solution which is bounded.
To solve the given differential equation |y| |y| = 0, we can break it down into two separate cases:
Case 1: y ≥ 0
In this case, the equation becomes y^2 = 0, which implies that y = 0 is the only solution.
Case 2: y < />
In this case, the equation becomes -y^2 = 0, which is not possible as the square of a negative number is always positive. Therefore, there are no solutions in this case.
Since the differential equation has different solutions for different cases, it does not have a general solution (option a) or a general solution with arbitrary constants (option b).
However, it is worth noting that the equation does have a particular solution y = 0, which satisfies the equation for both cases. This particular solution is bounded since it remains at zero for all values of x. Therefore, the correct answer is option c) particular solution which is bounded.
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Differential equation |y| + |y| = 0 hasa)GS solutionb)GS solution but no arbitrary constantc)particular solution which is boundedd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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