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प्रश्न
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
विकल्प
ex + e−y = C
ex + ey = C
e−x + ey = C
e−x + e−y = C
उत्तर
ex + e−y = C
We have,
\[\frac{dy}{dx} = e^{x + y} \]
\[ \Rightarrow \frac{dy}{dx} = e^x \times e^y \]
\[ \Rightarrow e^{- y} dy = e^x dx\]
Integrating both sides, we get
\[\int e^{- y} dy = \int e^x dx\]
\[ \Rightarrow - e^{- y} = e^x + D\]
\[ \Rightarrow e^x + e^{- y} = - D\]
\[ \Rightarrow e^x + e^{- y} = C ..........\left[\text{ Where, }C = - D \right]\]
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