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Pick the CORRECT solution for the following differential equation dy/dx = e^(x−y)

1. y = ln(e^x + Constant)
2. ln(y) = x + Constant
3. ln(y) = ln(e^x) + Constant
4. y = x + Constant

Correct answer: y = ln(e^x + Constant)

Solution

The correct option is derived from separating variables and integrating both sides of the equation. By rearranging and integrating, we find that the solution takes the form of y expressed as the natural logarithm of a function involving e raised to x plus a constant.

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