The solution of the differential equation $\sec^{2}x an y\ dx + \sec^{2}y an x\ dy = 0$ is

Question

The solution of the differential equation $\sec^{2}x	an y\ dx + \sec^{2}y	an x\ dy = 0$ is

Dr. Abubacker · Accepted Answer

(a)
Given, $\frac{\sec^{2}x}{	an x}dx = - \frac{\sec^{2}y}{	an y}dy$
$\Rightarrow$ $\int_{}^{}\frac{\sec^{2}x}{	an x}dx = - \int_{}^{}\frac{\sec^{2}y}{	an y}dy\$
Put $	an x = u$
$\Rightarrow$ $\sec^{2}x\ dx = du$
And $	an y = v$
$\Rightarrow$ $\sec^{2}y\ dy = dv$
$	herefore$ $\int_{}^{}\frac{du}{u} = - \int_{}^{}\frac{dv}{v}$
$\Rightarrow$ $\log u = - \log v + \log c \Rightarrow uv = c$
$	herefore$ $	an x.	an y = c$

Q. The solution of the differential equation $\sec^{2}x\tan y\ dx + \sec^{2}y\tan x\ dy = 0$ is

Explanation

Reviewed by Dr. Abubacker

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