Share

Books Shortlist

# 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

ConceptGeneral and Particular Solutions of a Differential Equation

#### 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?

#### Video TutorialsVIEW ALL [2]

Solution 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.
S