If $\cos \frac{y}{x} = A \log x + C$ is the general solution of $(x \sin \frac{y}{x}) dy = (y \sin \frac{y}{x} - x) dx$,then $A =$

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

The general solution of the differential equation $(3y - 7x + 7)dx + (7y - 3x + 3)dy = 0$ is

The general solution of the differential equation $\frac{dy}{dx} + \frac{x+y+1}{x-3y+5} = 0$ is

$I: y^{\prime}=\frac{y+x}{x} ; \quad II: y^{\prime}=\frac{x^2+y}{x^3} ; \quad III: y^{\prime}=\frac{2xy}{y^2-x^2}$
$S1$: Differential equations given by $I$ and $II$ are homogeneous differential equations.
$S2$: Differential equations given by $II$ and $III$ are homogeneous differential equations.
$S3$: Differential equations given by $I$ and $III$ are homogeneous differential equations.

If $y' = \frac{x - y}{x + y}$,then its solution is