The solution ...

Question

The solution of a differential equation $y^{''} + 3 y^{'} + 2 y = 0$ is of the form

c_{1} e^{x} + c_{2} e^{2 x}

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c_{1} e^{- x} + c_{2} e^{3 x}

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c_{1} e^{- x} + c_{2} e^{- 2 x}

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c_{1} e^{- 2 x} + c_{2} 2^{- x}

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Solution

The correct option is C $c_{1} e^{- x} + c_{2} e^{- 2 x}$
Given DE is $y^{''} + 3 y^{'} + 2 y = 0$
$\Rightarrow (D^{2} + 3 D + 2) y = 0$ ... (i)
$A E$ is $m^{2} + 3 m + 2 = 0$
$\Rightarrow m = - 1$ and $- 2$
General solution is
$∴ y = c_{1} e^{- x} + c_{2} e^{- 2 x}$

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