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Solution for 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 - CBSE (Science) Class 12 - Mathematics

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Question

The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
(a) ex + e−y = C
(b) ex + ey = C
(c) ex + ey = C
(d) e−x + e−y = C

Solution

(a) 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 for question: 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. For the courses CBSE (Science), CBSE (Commerce), CBSE (Arts), PUC Karnataka Science
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