JEE Advanced · MathematicsEasy

$Solve the differential equation \frac{d y}{d x} = e^{x + y} .$

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

Show correct answer & step-by-step solution

Correct answer: B — $- e^{- y} = e^{x} + C$

Solution

$Rewrite the equation as e^{- y} d y = e^{x} d x .$
$Integrate both sides: \int e^{- y} d y = \int e^{x} d x .$
$This yields - e^{- y} = e^{x} + C .$
$Hence the answer is (B).$

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