The differential equation, representing the curve $y = e^{x}(a\cos{x} + b\sin{x})$ where $a$ and $b$ are arbitrary constants, is

If $\frac{dy}{dx} = 2e^xy^3$, $y(0)= \frac{1}{2}$ then what is $4y^2(2-e^x)$ equal to?

Consider the following for the next items that follow:

A parabola passes through (1, 2) and satisfies the differential equation $\frac{d y}{d x}=\frac{2 y}{x}, x>0, y>0 .$