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Q)

Which of following satisfy the differential equation $y'+2xy=0?$

$(a)\;y=ce^{-x^2}, y'+2xy=0 \\ (b)\;y=x \log x-x,y'= \log x^2 \\ (c)\;y=\sin ^{-1}x, y''= \frac{x^2}{(1-x^2)^{3/2}}\\ (d)\;y=A e^{-1/x}, x^2y'-x-y=0 $

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A)
Check options and get answer like.
$y=ce^{-x^2}$
$\Rightarrow\:y'=-ce^{-x^2}.2x$
Substituting the values of $y\:and\:y'$ in the differential equation,
$\Rightarrow\:y'+2xy=-ce^{-x^2}.2x +2x ce^{-x^2}=0$
which satisfies the differential equation.
Hence (a ) is the correct answer.
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