Question

The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is

Options

• e^x + e^−y = C

• e^x + e^y = C

• e^−x + e^y = C

• e^−x + e^−y = C

Answer 1

e^x + 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

\[\int e^{- y} dy = \int e^x dx\]

\[ \Rightarrow - e^{- y} = e^x + D\]

\[ \Rightarrow e^x + e^{- y} = - D\]

\[ \Rightarrow e^x + e^{- y} = C ..........\left[\text{ Where, }C = - D \right]\]