The general solution of differential equation d y d x = e x + y is:

Question

The general solution of differential equation $\frac{d y}{d x} = e^{x + y}$ is:

Smart Achievers · Accepted Answer

(1)

Ans. $e^{x} + e^{- y} = C$

Explanation:

$\frac{d y}{d x} = e^{x} \times e^{y}$

$\Rightarrow$ $e^{- y} d y = e^{x} d x$

On integrating both sides,

$\Rightarrow$ $\int e^{- y} d y = \int e^{x} d x$

$\Rightarrow$ $- e^{- y} = e^{x} + A$

$\Rightarrow$ $- e^{- y} - e^{x} = A$

$\Rightarrow$ $e^{- y} + e^{x} = - A$

$e^{- y} + e^{x} = C,$ $where C = - A$

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