The solution of the differential equation $\frac{dy}{dx} = (1 + x)(1 + y^2)$ is

The general solution of the differential equation $y y^{\prime} = x \left[ \frac{y^2}{x^2} + \frac{\phi\left(\frac{y^2}{x^2}\right)}{\phi^{\prime}\left(\frac{y^2}{x^2}\right)} \right]$,where $\phi$ is an arbitrary function,is

Find the particular solution of the differential equation $\frac{dx}{dy} = \frac{\sin y(1 + y \cot y)}{x \log(x^2 e)}$,given that $y(1) = 0$.

The solution of the differential equation $\frac{dy}{dx} = \frac{x-y+3}{2(x-y)+5}$ is

The curve passing through the point $(1,2)$ given that the slope of the tangent at any point $(x, y)$ is $\frac{3x}{y}$ represents

The solution of the differential equation $\sqrt{a + x} \frac{dy}{dx} + xy = 0$ is