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

y^{''} = y

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y^{''} = y^{'}

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y^{''} + y = 0

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y^{''} + y^{'} = 0

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Solution

The correct option is A $y^{''} = y^{'}$
$y = c_{1} + c_{2} e^{x}$
$\Rightarrow y^{'} = c_{2} e^{x}$
$\Rightarrow y^{''} = c_{2} e^{x}$
$\Rightarrow y^{''} = y^{'}$

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