The general solution of the differential equation $2 dx + dy = (6xy + 4x - 3y) dx$ is

The solution of $\frac{dy}{dx} = \sqrt{1-y^2}$ with the initial condition $y(0) = 1$ is:

Let $y = y(x)$ be the solution curve of the differential equation $(1 + \sin x) \frac{dy}{dx} + (y + 1) \cos x = 0$ with the condition $y(0) = 0$. If the curve $y = y(x)$ passes through the point $(\alpha, -\frac{1}{2})$,then a value of $\alpha$ is:

The solution of $(x+y)^{2} \frac{dy}{dx} = a^{2}$ (where $a$ is a constant) is:

Find the general solution of the differential equation $\frac{dy}{dx} = \frac{1+y^2}{1+x^2}$.

The general solution of the differential equation $\frac{dy}{dx} = e^{x+y}$ is . . . . . . .