The differential equation which represents the family of curves

Question:

The differential equation which represents the family of curves $y=c_{1} e^{c_{2} x}$, where $c_{1}$ and $c_{2}$ are arbitrary constants, is :-

  1. $y^{\prime \prime}=y^{\prime}$

  2. $y y^{\prime \prime}=\left(y^{\prime}\right)^{2}$

  3.  $y^{\prime}=y^{2}$

  4. $y^{\prime \prime}=y^{\prime} y$

Correct Option: , 2

Solution:

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