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Question: The solution of the equation \(\frac{d^{2}y}{dx^{2}}\) = e<sup>–2x</sup> is –...

The solution of the equation d2ydx2\frac{d^{2}y}{dx^{2}} = e–2x is –

A

e−2x4\frac{e^{- 2x}}{4}

B

e−2x4\frac{e^{- 2x}}{4}+ cx + d

C

e−2x4\frac{e^{- 2x}}{4} + cx2 + d

D

14\frac{1}{4}e–2x + cx3 + d

Answer

e−2x4\frac{e^{- 2x}}{4}+ cx + d

Explanation

Solution

d2ydx2\frac{d^{2}y}{dx^{2}} = e–2x

Ž = e−2x2\frac{e^{- 2x}}{2} + c

Ž y = e−2x4\frac{e^{- 2x}}{4} + cx + d