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# The solution of the differential equation $\cot y dx=xdy$ is __________.

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• A linear differential equation of the form $\large\frac{dy}{dx}$$=f(x) can be solved by seperating the variables and then integrating it • \int \tan x=\log |\sec x|+c Given \cot y dx=x dy Seperating the variables we get, \large\frac{dy}{\cot y}=\large\frac{dx}{x}$$=> \tan y dy=\large\frac{dx}{x}$
On integrating we get,
$\int \tan y dy=\int \large\frac{dx}{x}$
$\log |\sec x|=\log x+\log c$
$\log c|\sec x|=\log x$
$=>x=c(\sec x)$
The solution of the differential equation
$\cot y dx=x dy$ is $x=c(\sec x)$
answered May 22, 2013 by

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