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CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Q191 Marksseparation

CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Question 19 (Differential Equations)

Assertion: \(e^x+e^{-y}=-2\) is a particular solution of \(dy/dx=e^{x+y}\). Reason: \(e^x+e^{-y}=C\) gives the general solution.

✅ Step-by-Step Solution

Final Answer: The assertion is false and the reason is true.
  1. Separate e⁻ʸ dy=eˣ dx and integrate to obtain eˣ+e⁻ʸ=C. The left side is positive for real x and y, so C=−2 is impossible.

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