If $\frac{dy}{dx} = y + 3$,$y + 3 > 0$ and $y(0) = 2$,then $y(\log 2)$ is equal to

If $y = f(x)$ is a monotonically increasing function such that $(\frac{dy}{dx})^2 = 6 - \frac{dy}{dx}$ and $y(0) = 5$, then $y(3) = ...$

General solution of the differential equation $\frac{dy}{dx} = \frac{x+y+1}{x+y-1}$ is given by

The solution of the differential equation $\frac{dy}{dx} = \frac{1 - 2y - 4x}{1 + y + 2x}$ is

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