Question

Assertion (A) : One of the particular solutions of the differential equation \( \frac{dy}{dx} = e^{x+y} \) can be \( e^x + e^{-y} = -2 \).
Reason (R) : \( e^x + e^{-y} = C \) is the general solution of the differential equation \( \frac{dy}{dx} = e^{x+y} \).

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

Always separate indices first when exponential functions contain sums: \( e^{x+y} \to e^x e^y \). This makes it easy to spot that the equation is solvable via direct variable separation.

Answer 1

The Correct Option is A