Use the method of Examples 5, 6, and 7 to find general solutions of the systems in Problems 11 through 20. If initial conditions are given, find the corresponding particular solution. For each problem, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system.

x' = 1/2y, y' = - 8x

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Example 5 Continued With initial values x (0) = 2, y (0) = 0, the general solution in Example 5 yields x (0) = A=2, y(0) = B = 0. The resulting particular solution is given by x(t) = 2 cost, y(t) = sint.