The general solution of the differential equation dydx-ex-y is

This equation can be written as dydx=e^xe^y e^ ydy=e^xdx Integrating both the sides, we get e^ y=e^x+c e^ y+e^x=C ...

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Standard XII

Mathematics

Variable Separable Method

The general s...

Question

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

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Solution

This equation can be written as
$\frac{d y}{d x} = e^{x} e^{y}$
$e^{- y} d y = e^{x} d x$
Integrating both the sides, we get
$- e^{- y} = e^{x} + c$
$e^{- y} + e^{x} = C$

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The general solution of the differential equation dydx=ex+y is

This equation can be written asdydx=exeye−ydy=exdxIntegrating both the sides, we get−e−y=ex+ce−y+ex=C

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

This equation can be written as
$\frac{d y}{d x} = e^{x} e^{y}$
$e^{- y} d y = e^{x} d x$
Integrating both the sides, we get
$- e^{- y} = e^{x} + c$
$e^{- y} + e^{x} = C$