Fi­nd an explicit solution of the given initial-value problem. Determine the exact interval I of definition by analytical methods. Use a graphing utility to plot the graph of the solution.

1. dy/dx = 2x + 1 / 2y, y(-2) = -1

2. (2y - 2)dy/dx 2x² + 4x + 2, y(1) = -2

3. e^y dx – e^-x dy = 0, y(0) = 0

4. sinx dx + y dy = 0, y(0) = 1