3. Consider the second order differential equation dx dx + 7- + 6x = 0. dt2...

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3. Consider the second order differential equation dx dx + 7- + 6x = 0. dt2 dt (a) Convert the equation to a 2 dimensional system. (b) Using a phase plane plotter, obtain the direction field. (c) Analytically find the solution that satisfies the initial condition r(0) = 2, x'(0) = -3 %3D (d) Plot that solution on your direction field. 3. Consider the second order differential equation dx dx + 7- + 6x = 0. dt2 dt (a) Convert the equation to a 2 dimensional system. (b) Using a phase plane plotter, obtain the direction field. (c) Analytically find the solution that satisfies the initial condition r(0) = 2, x'(0) = -3 %3D (d) Plot that solution on your direction field.