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General solution of differential equation $x dy -y dx=0$

$(a)\;\frac{x}{y}=c \\ (b)\;xy=c \\ (c)\;x^2-y^2=c \\ (d)\;x^2+y^2=c $
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$x dy =y dx$
$\large\frac{dy}{y}=\frac{dx}{x}$
$\log x -\log y =\log (\large\frac{x}{y})$
$\log y =\log x +c_1$
$\log (\large\frac{y}{n})$$=c_1$
or $ -c_1=-\log (\large\frac{y}{x})$
$ \large\frac{y}{x}$$=c$
or $ -c_1=-\log (\large\frac{x}{y})$
$\large\frac{x}{y} =\frac{1}{c}$
$\large\frac{x}{y}$$=c_2$
$\large\frac{x}{y}$$=c_3$
Hence a is the correct answer
answered Feb 3, 2014 by meena.p
 

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