Question: Consider the differential equation y + 6y + 13y = 0. (a) Show that y1(t) = e-3t cos(2t) and y2(t) = e-3t sin(2t) are

Consider the differential equation y" + 6y + 13y = 0. (a)

Consider the differential equation y" + 6y + 13y = 0. (a) Show that y1(t) = e-3t cos(2t) and y2(t) = e-3t sin(2t) are two solutions of this equation. (b) Compute the Wronskian of the solutions in part (a) and use it to show that y(t) and 2(t) are linearly independent. (c) Write the general solution of this equation.

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