Question

The general solution of the differential equation, $\sin 2x\left(\frac{dy}{dx}-\sqrt{\tan x}\right)-y=0$, is

• A. $y\sqrt{\tan x}=\cot x+C$
• B. $y\sqrt{\cot x}=\tan x+C$
• C. $y\sqrt{\cot x}=x+C$
• D. $y\sqrt{\tan x}=x+C$

Answer 1

Answer: (C)

$\sin 2x\left(\frac{dy}{dx}-\sqrt{\tan x}\right)-y=0$
$\frac{dy}{dx}-(\mathrm{cosec}2x)y=\sqrt{\tan x}$
IF $=e^{\int -\mathrm{cosec}2xdx}=e^{-\frac{1}{2}\ln \tan x}=\sqrt{\cot x}$
so solution is
$y\sqrt{\cot x}=\int 1dx$
$y\sqrt{\cot x}=x+C$