Question

The general solution of the differential equation $\frac{dy}{dx}=\frac{1-x}{y}$ is a family of curves which looks most like which of the following?

Answer 1

$\frac{dy}{dx}=\frac{1-x}{y}$

$ydy=\left(1-x\right)dx$

$\frac{y^2}{2}=x-\frac{x^2}{2}+c$

$or{y}^2=2x-x^2+2c$

$x^2+y^2-2x=k2c=k$

${\left(x-1\right)}^2+y^2-1=k$

$or{\left(x-1\right)}^2+y^2=k+1\to Equationofcircle$

$\therefore Option\left(B\right)$