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If xy=e(x-y), (dy/dx)=
  • a)
    [(y)/(1+logx)]
  • b)
    [(x-y)/(1+logx)2]
  • c)
    [(x-y)/(1+logx)]
  • d)
    [(logx)/(1+logx)2]
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If xy=e(x-y), (dy/dx)=a)[(y)/(1+logx)]b)[(x-y)/(1+logx)2]c)[(x-y)/(1+l...
Explanation:

Given Differential Equation:
xy = e(x-y)

Step 1: Differentiate both sides with respect to x using product rule.
d(xy)/dx = d(e(x-y))/dx
y + x(dy/dx) = e(x-y)(1 - dy/dx)

Step 2: Solve for (dy/dx).
x(dy/dx) = e(x-y) - y - e(x-y)(dy/dx)
x(dy/dx) + e(x-y)(dy/dx) = e(x-y) - y
(dy/dx)(x + e(x-y)) = e(x-y) - y
dy/dx = (e(x-y) - y)/(x + e(x-y))

Step 3: Simplify the expression.
dy/dx = (e(x-y) - y)/(x + e(x-y))
dy/dx = (e(x-y) - y)/(1 + e(x-y)/x)
dy/dx = (e(x-y) - y)/(1 + e(x-y)log(x))
Therefore, the correct answer is option D [(logx)/(1+logx)^2].
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If xy=e(x-y), (dy/dx)=a)[(y)/(1+logx)]b)[(x-y)/(1+logx)2]c)[(x-y)/(1+logx)]d)[(logx)/(1+logx)2]Correct answer is option 'D'. Can you explain this answer?
Question Description
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