The solution of the equation d y-d x-ex-y-x2 e-y is -MP PET 2004-A- ey-ex-x3-3-cB- ey-ex-2 x-cC- ey-ex-x3-cD- y-ex-c

The correct option is A 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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Byju's Answer

Standard XII

Mathematics

Degree of a Differential Equations

The solution ...

Question

The solution of the equation $\frac{d y}{d x} - e^{x - y} + x^{2} e^{- y}$ is
[MP PET 2004]

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Solution

The correct option is A

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

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Similar questions

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 $\frac{d y}{d x} = e^{x + y}$ 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. If

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

, show that

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

Q. Find

\frac{d y}{d x}

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

Q. If

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

, find

\frac{d y}{d x}

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The solution of the equation dydx−ex−y+x2 e−y is [MP PET 2004]

The correct option is A dydxex−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
[MP PET 2004]

The correct option is A

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