$A$ bag contains $3$ red,$6$ white,and $7$ blue balls. Two balls are drawn one after another. What is the probability that the first ball is white and the second ball is blue,if the first ball drawn is not replaced in the bag?

Find the solution of the following differential equation: $\{x \cos (y/x) + y \sin (y/x)\} y dx = \{y \sin (y/x) - x \cos (y/x)\} x dy$.

If the solution curve $y=y(x)$ of the differential equation $y^{2} dx + (x^{2} - xy + y^{2}) dy = 0$ passes through the point $(1, 1)$ and intersects the line $y = \sqrt{3}x$ at the point $(\alpha, \sqrt{3}\alpha)$,then the value of $\log_{e}(\sqrt{3}\alpha)$ is equal to

Let the solution curve of the differential equation $x dy = (\sqrt{x^{2}+y^{2}}+y) dx$,$x > 0$,intersect the line $x = 1$ at $y = 0$ and the line $x = 2$ at $y = \alpha$. Then the value of $\alpha$ is.

Let $y=y(x)$ be the solution of the differential equation $x \tan \left(\frac{y}{x}\right) d y=\left(y \tan \left(\frac{y}{x}\right)-x\right) d x$ for $-1 \leq x \leq 1$,with the initial condition $y\left(\frac{1}{2}\right)=\frac{\pi}{6}$. Then the area of the region bounded by the curves $x=0$,$x=\frac{1}{\sqrt{2}}$,and $y=y(x)$ in the upper half plane is:

The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) dy = \left(y \sin \frac{y}{x} - x\right) dx$ is