The general solution of the differential equation log dydx - x - y is

The correct option is B e^x+e^ y=c log (dy/dx) = x+y dy/dx = e^x+y ∫dy/e^y = ∫ e^xdx e^ y/ 1 = e^x+c_1 e^x+e^ y = c ...

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Byju's Answer

Standard XII

Mathematics

Linear Differential Equations of First Order

The general s...

Question

The general solution of the differential equation $log (\frac{d y}{d x}) = x + y$ is

e^{x} + e^{y} = c

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e^{x} + e^{- y} = c

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e^{- x} + e^{y} = c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

e^{- x} + e^{- y} = c

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Solution

The correct option is B $e^{x} + e^{- y} = c$
$l o g (\frac{d y}{d x}) = x + y$
$\frac{d y}{d x} = e^{x + y}$
$\int \frac{d y}{e^{y}} = \int e^{x} d x$
$\frac{e^{- y}}{- 1} = e^{x} + c_{1}$
$e^{x} + e^{- y} = c$

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Similar questions

The general solution of the differential equation $\frac{d y}{d x} = e^{x + y}$ is
(a) $e^{x} + e^{- y} = C$
(b) $e^{x} + e^{y} = C$
(c) $e^{- x} + e^{y} = C$
(d) $e^{- x} + e^{- y} = C$

Q. The general solution of the differential equation

\frac{d y}{d x} = e^{x + y}

, is
(a) e^x+ e^−y = C
(b) e^x + e^y = C
(c) e⁻^x + e^y = C
(d) e^−x + e^−y = C

The general solution of the differential equation $e^{x} d y + (y e^{x} + 2 x) d x = 0$ is

a) $x e^{y} + x^{2} = C$

b) $x e^{y} + y^{2} = C$

c) $y e^{x} + x^{2} = C$

d) $y e^{y} + x^{2} = C$

Q. Which of the following relation in x and y is general solution of the differential equation

\frac{d y}{d x} = y

Q. Which of the following relation in x and y is general solution of the differential equation

\frac{d y}{d x} = y

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The general solution of the differential equation log(dydx)=x+y is

The correct option is B ex+e−y=clog(dydx)=x+ydydx=ex+y∫dyey=∫exdxe−y−1=ex+c1ex+e−y=c

The general solution of the differential equation $log (\frac{d y}{d x}) = x + y$ is

The correct option is B $e^{x} + e^{- y} = c$
$l o g (\frac{d y}{d x}) = x + y$
$\frac{d y}{d x} = e^{x + y}$
$\int \frac{d y}{e^{y}} = \int e^{x} d x$
$\frac{e^{- y}}{- 1} = e^{x} + c_{1}$
$e^{x} + e^{- y} = c$