The solution of the equation $\frac{d^2 y}{d x^2}=e^{-2 x}$

The solution of the equation $\frac{d^2 y}{d x^2}=e^{-2 x}$
  1. $\frac{e^{-2 x}}{4}$
  2. $\frac{e^{-2 x}}{4}+c x+d$
  3. $\frac{1}{4} e^{-2 x}+c x^2+d$
  4. $\frac{1}{4} e^{-4 x}+c x+d$

Solution

$\frac{d^2 y}{d x^2}=e^{-2 x} ; \frac{d y}{d x}=\frac{e^{-2 x}}{-2}+c ; y=\frac{e^{-2 x}}{4}+c x+d$

Asked in: JEE Main 2002

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