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Formation of a Differential Equation from a General Solution

The D.E whose...

Question

The D.E whose solution in $y = c e^{x}$ is?

A

y_{1} = y^{2}

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B

y_{2} = y_{1}

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C

y_{1} = y

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D

y_{1} + y = 0

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Solution

The correct option is C $y_{1} = y$
$y = c e^{x} \frac{d y}{d x} = c e^{x} \frac{d y}{d x} = y$
$\Rightarrow y_{1} = y$

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