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The differential equation | d y d x | + | y | + 3 = 0 admits
- a)Infinite number of solutions
- b)No solution
- c)A unique solution
- d)Many solutions
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The differential equation | d y d x | + | y | + 3 = 0 admitsa)Infinite...
Explanation:
Given differential equation is |d/dx| |y| + 3 = 0
Let's consider two cases:
Case 1: d/dx > 0 (when y > 0)
In this case, the differential equation becomes d/dx(y) + 3 = 0
Solving this differential equation gives y = ce^(-3x), where c is a constant
Case 2: d/dx < 0="" (when="" y="" />< />
In this case, the differential equation becomes d/dx(-y) + 3 = 0
Solving this differential equation gives y = -ce^(3x), where c is a constant
Conclusion:
As we can see, the solutions obtained in the two cases are not continuous at y = 0, which means there is no solution that satisfies the given differential equation for all values of x. Therefore, the correct answer is option B, i.e., there is no solution.
Given differential equation is |d/dx| |y| + 3 = 0
Let's consider two cases:
Case 1: d/dx > 0 (when y > 0)
In this case, the differential equation becomes d/dx(y) + 3 = 0
Solving this differential equation gives y = ce^(-3x), where c is a constant
Case 2: d/dx < 0="" (when="" y="" />< />
In this case, the differential equation becomes d/dx(-y) + 3 = 0
Solving this differential equation gives y = -ce^(3x), where c is a constant
Conclusion:
As we can see, the solutions obtained in the two cases are not continuous at y = 0, which means there is no solution that satisfies the given differential equation for all values of x. Therefore, the correct answer is option B, i.e., there is no solution.
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The differential equation | d y d x | + | y | + 3 = 0 admitsa)Infinite number of solutionsb)No solutionc)A unique solutiond)Many solutionsCorrect answer is option 'B'. Can you explain this answer?
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