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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

y = 14e–2x\frac{1}{4}e^{–2x}

B

y = 14e–2x\frac{1}{4}e^{–2x}+ cx + d

C

y =14e–2x\frac{1}{4}e^{–2x} + cx2 + d

D

y = 14e–2x\frac{1}{4}e^{–2x} + c + d

Answer

y = 14e–2x\frac{1}{4}e^{–2x}+ cx + d

Explanation

Solution

Integrate dy/dx = –e–2x/2 + c

again Integrate y = e–2x/4 + cx + d