The general solution of the differential equation d y-d x-2 y-e-2 x is A- y - Ce -2 xB- y-x e-2 x-C e-2 xC- y - xe -2 x - CD- y - e -2 x - C

The correct option is B y = xe^ 2x + C e^ 2xdy/dx + 2y = e^ 2x Integrating factor = e^∫ 2 dx = e^2x Solution of the D.E, y· e^2x = ∫ e^ 2x× e^2x dx ⇒ nbsp; ...

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Standard XII

Mathematics

Higher Order Derivatives

The general s...

Question

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

y = C e^{- 2 x}

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y = x e^{- 2 x} + C e^{- 2 x}

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y = x e^{- 2 x} + C

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y = e^{- 2 x} + C

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Solution

The correct option is B $y = x e^{- 2 x} + C e^{- 2 x}$
$\frac{d y}{d x} + 2 y = e^{- 2 x}$
Integrating factor
$= e^{\int 2 d x} = e^{2 x}$
Solution of the D.E,
$y \cdot e^{2 x} = \int e^{- 2 x} \times e^{2 x} d x \Rightarrow y \cdot e^{2 x} = x + C \Rightarrow y = x \cdot e^{- 2 x} + C e^{- 2 x}$

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The general solution of the differential equation dydx+2y=e−2x is

The correct option is B y=xe−2x+Ce−2xdydx+2y=e−2x Integrating factor =e∫2 dx=e2x Solution of the D.E, y⋅e2x=∫e−2x×e2x dx⇒y⋅e2x=x+C⇒y=x⋅e−2x+Ce−2x

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

The correct option is B $y = x e^{- 2 x} + C e^{- 2 x}$
$\frac{d y}{d x} + 2 y = e^{- 2 x}$
Integrating factor
$= e^{\int 2 d x} = e^{2 x}$
Solution of the D.E,
$y \cdot e^{2 x} = \int e^{- 2 x} \times e^{2 x} d x \Rightarrow y \cdot e^{2 x} = x + C \Rightarrow y = x \cdot e^{- 2 x} + C e^{- 2 x}$