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The particular solution of

$$\log_{e}\left ( \frac{dy}{dx} \right ) = 5x + 7y, \;y(0)= 0$$

is.

  1. $e^{5x}+5e^{-7y}=7$

  2. $7e^{5x}-5e^{-7y}=5$

  3. $5e^{5x}+7e^{7y}=12$

  4. $7e^{5x}+5e^{-7y}=12$

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