If $\log y$ is an integrating factor of $\frac{dx}{dy} + P(y)x = Q(y)$,then $P(y) =$

Find the equation of a curve passing through the origin,given that the slope of the tangent to the curve at any point $(x, y)$ is equal to the sum of the coordinates of the point.

An integrating factor of the differential equation $\left(1-x^2\right) \frac{d y}{d x}+x y=\frac{x^4}{\left(1+x^5\right)}\left(\sqrt{1-x^2}\right)^3$ is

The solution of $\cos y + (x \sin y - 1) \frac{dy}{dx} = 0$ is

Integrating factor of $(x+2 y^3) \frac{d y}{d x}=y^2$ is

Let $\alpha x = \exp(x^\beta y^\gamma)$ be the solution of the differential equation $2x^2 y \frac{dy}{dx} - (1 - xy^2) = 0$,for $x > 0$ and $y(2) = \sqrt{\log_e 2}$. Then $\alpha + \beta - \gamma$ equals: