If $P(A') = 0.6$,$P(B) = 0.8$,and $P(B/A) = 0.3$,then $P(A/B) = $

Let $y(x)$ be the solution of the differential equation $x^2 \frac{dy}{dx} + xy = x^2 + y^2$,$x > \frac{1}{e}$,satisfying $y(1) = 0$. Then the value of $2 \frac{(y(e))^2}{y(e^2)}$ is $....$

The equation of the curve satisfying $x dy - y dx = \sqrt{x^2 - y^2} dx$ with the condition $y(1) = 0$ is:

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

The solution of the differential equation $y \frac{dy}{dx} = x \left[ \frac{y^2}{x^2} + \frac{\phi(y^2/x^2)}{\phi'(y^2/x^2)} \right]$ is (where $c$ is a constant):

The solution of the equation $\frac{dy}{dx} = \frac{x}{2y - x}$ is