Question

The general solution of the differential equation $\frac{dy}{dx}+y\cot x=\sec x$ is

• A. $y\cos x=\ln |\sec x|+C$
• B. $y\sin x=\ln |\sec x|+C$
• C. $y\sin x=\ln |\sin x|+C$
• D. $y\sin x=\ln |\cos x|+C$

Answer 1

The correct option is B $y\sin x=\ln |\sec x|+C$

$\frac{dy}{dx}+y\cot x=\sec x$
Integrating factor
$=e^{\int \cot xdx}=e^{\ln \sin x}=\sin x$
Solution of D.E,
$y\sin x=\int \sec x\cdot \sin xdx+C\Rightarrow y\sin x=\int \tan xdx+C\Rightarrow y\sin x=\ln |\sec x|+C$