The solution of the differential equation $\frac{d^{2}y}{dx^{2}} = e^{- 2x}$ is $y = c_{1}e^{- 2x} + c_{2}x + x_{3}$, where $c_{1}$ is

Question

Dr. Abubacker · Accepted Answer

(b)
Given, $\frac{d^{2}y}{dx^{2}} = e^{- 2x}$
$\Rightarrow$ $\frac{dy}{dx} = - \frac{e^{- 2x}}{2} + c_{2}$ [integrating]
$\Rightarrow$ $y = \frac{e^{- 2x}}{4} + c_{2}x + c_{3}$ [integrating]
But $y = c_{1}e^{- 2x} + c_{2}x + c_{3}$ [given]
$	herefore$ $c_{1} = \frac{1}{4}$

Q. The solution of the differential equation $\frac{d^{2}y}{dx^{2}} = e^{- 2x}$ is $y = c_{1}e^{- 2x} + c_{2}x + x_{3}$, where $c_{1}$ is

Explanation

Reviewed by Dr. Abubacker

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