Solution of $\frac{d y}{d x}=\frac{y}{x}+\tan \frac{y}{x}$ is :
Answer & explanation
Correct answer: option 1
$\frac{d y}{d x}=\frac{y}{x}+\tan \frac{y}{x}$
put $y=vx \Rightarrow v+x \frac{d v}{d x}=v+\tan v$
$\cot v dv=\frac{d x}{x}$
Integrating, we get $\ln \sin v=\ln x+\ln k \Rightarrow \sin \frac{y}{x}=k x$
Hence (1) is the correct answer.