$\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 $x = 0$ and $y = 0$, represents which of the following curves?

Let $A$ and $B$ be two independent events. If $P(A) = \frac{1}{5}$ and $P(A \cup B) = \frac{7}{10}$,then what is the value of $P(\overline{B})$?

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

The general solution of $y^2 dx + (x^2 - xy + y^2) dy = 0$ is:

The solution of the differential equation $3 x y' - 3 y + (x^2 - y^2)^{1/2} = 0$, satisfying the condition $y(1) = 1$ is