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BITSAT2019MathematicsDifferential EquationsActual

Solution of the equation d y d x = e x - y e x - e y is

Options

  1. Ae y = e x - 1 + c e - e x
  2. Be y - x = - 1 + c e - e x
  3. Ce x + e y = c e - e x
  4. DNone of these

Correct answer

A. e y = e x - 1 + c e - e x

Step-by-step solution

We have, d y d x = e x - y e x - e y ⇒   e y d y d x + e y e x = e 2 x Put e y = v ∴   e y d y d x = d v d x ∴   d v d x + v e x = e 2 x This is linear equation I . F = = e ∫ e x d x = e e x ∴ Required solution is v · e e x = ∫ e e x · e 2 x d x + C v · e e x = e e x e x - 1 + C ⇒   e y · e e x = e e x e x - 1 + C ⇒   e y = e x - 1 + c e - e x

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