Question

The general solution of \( \frac{dy}{dx} = e^{x - y} \) is:

• A. $e^y = e^x + c$
• B. $e^{-y} = e^x + c$
• C. $e^y = e^{-x} + c$
• D. $y = x + c$

Hint:

Remember: $e^{a-b} = e^a \cdot e^{-b}$. This allows you to separate the x and y variables easily.

Answer 1

The Correct Option is A

Step 1: Concept
Use the variable separable method. $e^{x-y} = e^x / e^y$.
Step 2: Analysis
$e^y dy = e^x dx$.
Integrating both sides: $\int e^y dy = \int e^x dx$.
Step 3: Conclusion
$e^y = e^x + c$.
Final Answer: (A)