Let x and y be functions of t. Find the general solution of the system of equations below by first converting the system into second-order differential equations involving only y and only x. Find a particular solution for the initial conditions. Use a comput system or graphing calculator to construct a direction field and typical solution curves for the given system. x' = y, y'=20x-y; x(0) = 5, y(0)=2 Solve for x(t). Choose the correct answer below. -5t+ - 5t + Be x(t) = A e x(t) = A e 4t+Be-5t C. x(t) = A cos (-5t) + B sin (-5t) - 5t -5t + Bt e x(t) = Ae Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations.

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