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NDA 2026 · PYQ · Differential Equations · medium

Consider the differential equation e^(x+y) dy/dx = e^(x-y). What is the solution of the differential equation with y(0) = 0?

  1. A.y = ln(2x + 1)
  2. B.y = ln(2x - 1)
  3. C.2y = ln(2x + 1)✓ Correct
  4. D.2y = ln(2x - 1)

Explanation

From dy/dx = e^(-2y), separating variables: e^(2y) dy = dx. Integrating: e^(2y)/2 = x + C. At y(0) = 0: 1/2 = C. So e^(2y)/2 = x + 1/2, giving e^(2y) = 2x + 1, hence 2y = ln(2x + 1).
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