The differential equation corresponding to primitive \( \mathrm{P} ...

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The differential equation corresponding to primitive
\( \mathrm{P} \) \( y=e^{c x} \) is

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or
The elimination of the arbitrary constant \( m \) from the equation \( y=e^{m x} \) gives the differential equation
(1) \( \frac{d y}{d x}=\left(\frac{y}{x}\right) \log x \)
(2) \( \frac{d y}{d x}=\left(\frac{x}{y}\right) \log y \)
(3) \( \frac{d y}{d x}=\left(\frac{y}{x}\right) \log y \)
(4) \( \frac{d y}{d x}=\left(\frac{x}{y}\right) \log x \)
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