Which of the following is-are a solution of the differential equation d y d x-e x -A- y-e xB- y - e - xC- y-e x-1D- y- e - x -1

Y=fx nbsp;is nbsp;a nbsp;solution nbsp;of nbsp;the nbsp;differentialequation nbsp;if nbsp;it nbsp;satisfies nbsp;the nbsp;equation.Substit ...

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Standard XII

Mathematics

Ordinary Differential Equations

Which of the ...

Question

$Which of the following is/are a solution of the differential equation \frac{dy}{dx} = e^{x} ?$

{y = e}^{x}

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{y = e}^{- x}

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{y = e}^{x} +1

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{y = e}^{- x} -1

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Solution

The correct options are
A ${y = e}^{x}$
C ${y = e}^{x} +1$
$y = f (x) is a solution of the differential equation if it satisfies the equation . Substitute each of the given y (x) in the DE to find out which is / are the solution (s) . For y = e^{x}, \frac{dy}{dx} = \frac{d (e^{x})}{dx} = e^{x} which is equal to the RHS of the DE . Hence y = e^{x} is a solution of the given DE . For y = e^{- x}, \frac{dy}{dx} = \frac{d (e^{- x})}{dx} = - e^{- x} which is not equal to the RHS of the DE . Hence y = e^{- x} is not a solution of the given DE . Similarly we can check for the other 2 options .$

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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

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

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

Q. The solution of the differential equation

\frac{d y}{d x} + 1 = e^{x + y}

, is
(a) (x + y) e^x^{+ y} = 0
(b) (x + C) e^x^{+ y} = 0
(c) (x − C) e^x^{+ y} = 1
(d) (x − C) e^x^{+ y}+ 1 =0

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

y + \sqrt{1 + y^{2}} = e^{x},

then the value of

y

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Which of the following is/are a solution of the differential equation dydx=ex ?

$Which of the following is/are a solution of the differential equation \frac{dy}{dx} = e^{x} ?$