$\frac{dy}{dx} = \frac{y + x \tan(\frac{y}{x})}{x} \Rightarrow \sin(\frac{y}{x}) = $

The solution of the differential equation $\frac{dy}{dx} = \frac{x - y}{x + y}$, with the initial condition $y(0) = 0$, represents which of the following curves?

If $x \frac{dy}{dx} = y(\log y - \log x + 1)$,then the general solution of this equation is

If $A$ and $B$ are two events such that $P(A) = \frac{1}{3}$,$P(B) = \frac{1}{5}$,and $P(A \cup B) = \frac{1}{2}$,then $P(A \mid B') + P(B \mid A')$ is equal to

The general solution of $\left(1+e^{\frac{x}{y}}\right) d x+e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) d y=0$ is

The general solution of $x \frac{dy}{dx} = y - x \tan \left( \frac{y}{x} \right)$ is . . . . . .