#### Question

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

e

^{x}^{ }+ e^{−y}= Ce

^{x}+ e^{y}= Ce

^{−}^{x}+ e^{y}= Ce

^{−x}+ e^{−y}= C

#### Solution

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

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

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

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

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

Is there an error in this question or solution?

Solution The General Solution of the Differential Equation D Y D X = E X + Y , is Concept: General and Particular Solutions of a Differential Equation.