Solution of the differential equation $\frac{x d y}{x^2+y^2}=\left(\frac{y}{x^2+y^2}-1\right) d x$, is
Answer & explanation
Correct answer: option 1
The given differential equation can be written as
$\frac{x d y-y d x}{x^2+y^2}=-d x \Rightarrow d\left\{\tan ^{-1}\left(\frac{y}{x}\right)\right\}=-d x$
On integrating, we obtain
$\tan ^{-1}\left(\frac{y}{x}\right)=-x+f C$, which is the required solution.