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# The General Solution of the Differential Equation D Y D X = E X + Y , is - CBSE (Commerce) Class 12 - Mathematics

ConceptGeneral and Particular Solutions of a Differential Equation

#### Question

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

• ex + e−y = C

• ex + ey = C

• ex + ey = C

• e−x + e−y = C

#### Solution

ex + 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

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

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

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

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

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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.
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