The solution of the differential equation,$y\,dx + (x + x^2y)dy = 0$ is

If $y(x)$ is the solution of the differential equation $x dy - (y^2 - 4y) dx = 0$ for $x > 0$ and $y(1) = 2$,and the slope of the curve $y = y(x)$ is never zero,then the value of $10y(\sqrt{2})$ is . . . .

Which of the following is true for $y(x)$ that satisfies the differential equation $\frac{dy}{dx} = xy - 1 + x - y$ with the initial condition $y(0) = 0$?

If $2 f(x) = f^{\prime}(x)$ and $f(0) = 3$,then the value of $f(2)$ is

If $\frac{dy}{dx} = 1 + x + y + xy$ and $y(-1) = 0$,then the function $y$ is

If the differential equation $\frac{dy}{dx} + \frac{x}{y} = \frac{a}{y}$,where $a$ is a constant,represents a family of circles,then the radius of the circle is ......