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Differential Equations

Variable Separable Form

Premium Question

Grade 12

Question:

The general solution of $\frac{dy}{dx} = e^{x+y}$ is:

(1) $e^x - e^{-y} = C$

(2) $e^x + e^{-y} = C$

(3) $e^{x+y} = C$

(4) $e^{-x} + e^y = C$

Step-by-Step Solution

Key Concept: Write $e^{x+y} = e^x \cdot e^y$ and separate the variables as $e^{-y} \, dy = e^x \, dx$, then integrate both sides.

The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.

Correct Answer: (2)