The general form of a linear, homogeneous, second-order equation with constant coefficients is (d^2 y/dt^2) + p(dy/dt) + qy = 0. (a) Write the first-order system for this equation, and write this system in matrix form. (b) Show that if q does not = 0, then the origin is the only equilibrium point of the system. (c) Show that if q does not = 0, then the only solution of the second-order equation with y constant is y(t) = 0 for all t.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.