The D.E whose solution is $y = C_{1} e^{2 x} + C_{2} e^{- 2 x}$ is:

y_{2} = 2 y

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y_{2} = y

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y_{2} = 3 y

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y_{2} = 4 y

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Solution

The correct option is D $y_{2} = 4 y$
$y = C_{1} e^{2 x} + C_{2} e^{- 2 x}$
$\Rightarrow y_{1} = 2 C_{1} e^{2 x} - 2 C_{2} e^{- 2 x}$
$y_{2} = 4 C_{1} e^{2 x} + 4 C_{2} e^{- 2 x}$
$\Rightarrow y_{2} = 4 y$

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