If $y=a e^x+b e^{-x}+c$, where $a, b, c$ are parameters, then $y^{\prime \prime \prime}$ is equal to

If $y=a e^x+b e^{-x}+c$, where $a, b, c$ are parameters, then $y^{\prime \prime \prime}$ is equal to
  1. $0$
  2. $y$
  3. $y^{\prime}$
  4. $y^{\prime \prime}$

Solution

We have, $ \begin{aligned} y & =a e^x+b e^{-x}+c \\ y^{\prime} & =a e^x-b e^{-x} \\ y^{\prime \prime} & =a e^x+b e^{-x} \\ y^{\prime \prime \prime} & =a e^x-b e^{-x}=y^{\prime} \end{aligned} $

Asked in: AP EAMCET 2002

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