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

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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

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

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

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

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

  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.
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