The solution of the equation dy-dx - ex-y - x2 e-y is

Dy/dx =e^x y + x^2 e^ y = e^ y (e^x + x^2) ⇒ e^y dy = (x^2 + e^x)dx Now integrating both sides, we Get e^y = x^3/3 + e^x + c. ...

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Standard XI

Chemistry

Synthesis of Amides

The solution ...

Question

The solution of the equation $\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}$ is

$e^{y} = e^{x} + \frac{x^{3}}{3} + c$

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

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$e^{y} = e^{x} + x^{3} + c$

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$y = e^{x} + c$

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Solution

The correct option is A
$e^{y} = e^{x} + \frac{x^{3}}{3} + c$

$\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y} = e^{- y} (e^{x} + x^{2}) \Rightarrow e^{y} d y = (x^{2} + e^{x}) d x$
Now integrating both sides, we
Get $e^{y} = \frac{x^{3}}{3} + e^{x} + c .$

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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 solution of the differential equation

\frac{d y}{d x} = 2 e^{x - y} + x^{2} e^{- y}

The general solution of differential equation $\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}$ is

Q. Solution of the differential equation

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Q. The general solution of the differential equation

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

is :

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The solution of the equation dydx=ex−y+x2 e−y is

The correct option is A ey=ex+x33+c dydx=ex−y+x2 e−y=e−y(ex+x2)⇒ey dy=(x2+ex)dx Now integrating both sides, we Get ey=x33+ex+c.

The solution of the equation $\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}$ is

The correct option is A
$e^{y} = e^{x} + \frac{x^{3}}{3} + c$

$\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y} = e^{- y} (e^{x} + x^{2}) \Rightarrow e^{y} d y = (x^{2} + e^{x}) d x$
Now integrating both sides, we
Get $e^{y} = \frac{x^{3}}{3} + e^{x} + c .$