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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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The solution of the differential equation $\cot y dx=xdy$ is __________.

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Toolbox:
  • 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 meena.p
 
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