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

  • Option 1)

    \frac{1}{4}e^{-2x}\;

  • Option 2)

    \; \frac{1}{4}e^{-2x}+cx+d\;

  • Option 3)

    \; \; \frac{1}{4}e^{-2x}+cx^{2}+d\;

  • Option 4)

    \; \; \frac{1}{4}e^{-2x}+c+d\;

 

Answers (1)

As we learnt in 

Solution of differential equations -

A function y =f(x) is a solution of differential equation, if the substitution of f(x) and its derivative (s) in differential equation reduces it to an identity.

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\frac{d^{2}y}{dx^{2}}=e^{-2x}

\frac{dy}{dx}=\frac{e^{-2x}}{-2}+C

\int dy = -\frac{1}{2}\:\int e^{-2x}dx+cx+d

y=\frac{1}{4}\:e^{-2x}\:+cx+d


Option 1)

\frac{1}{4}e^{-2x}\;

This option is incorrect.

Option 2)

\; \frac{1}{4}e^{-2x}+cx+d\;

This option is correct.

Option 3)

\; \; \frac{1}{4}e^{-2x}+cx^{2}+d\;

This option is incorrect.

Option 4)

\; \; \frac{1}{4}e^{-2x}+c+d\;

This option is incorrect.

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