If $\frac{dy}{dx} = \frac{xy + y}{xy + x}$,then the solution of the differential equation is:

Let $y=y(x)$ be a solution curve of the differential equation,$(1-x^2 y^2) dx = y dx + x dy$. If the line $x = 1$ intersects the curve $y = y(x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y(x)$ at $y = \alpha$,then a value of $\alpha$ is

Find the general solution of the differential equation: $x^{5} \frac{dy}{dx} = -y^{5}$

The particular solution of the differential equation $\frac{dy}{dx} = \sec y$ with the initial condition $y(0) = 0$ is:

The solution of $x^2 + y^2 \frac{dy}{dx} = 4$ is

The solution of the differential equation $(\sin x + \cos x)dy + (\cos x - \sin x)dx = 0$ is