Problem

For each of the following differential equations, find the general solution and sketch the family of solution curves. a.

\frac{dy}{dx} = 2x

\frac{dy}{dx} = y

\frac{dy}{dx} = \frac{2y}{x}

\frac{dy}{dx} = \frac{x}{y}

\frac{dy}{dx} = \cos x

\frac{dy}{dx} = y \cot x, \quad 0 < x < \pi