#### Question

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

(a) e^{x}^{ }+ e^{−y} = C

(b) e^{x} + e^{y} = C

(c) e^{−}^{x} + e^{y} = C

(d) e^{−x} + e^{−y} = C

#### Solution

(a) 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 (a) ex + e−y = C (b) ex + ey = C (c) e−x + ey = C (d) e−x + e−y = C Concept: General and Particular Solutions of a Differential Equation.