The general solution of the differential equation \(\displaystyle\frac{dy}{dx}=e^{x+y}\), is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(e^x+e^{-y}=c\)
Since \(e^{x+y} = e^x e^y\), the variables separate:
\( \displaystyle \frac{dy}{dx} = e^x e^y \)
\(e^{-y}\,dy = e^x\,dx\)
Integrating both sides:
\(-e^{-y} = e^x + k\)
\(e^x + e^{-y} = -k\)
Writing the constant −k as c:
\(e^x + e^{-y} = c\)
NCERT (2026-27 edition):
Differential Equations with Variables Separable
