A coupled spring mass system in the presence of an external driving field has the equations of motion 2x"(t) + 6x(t) – 2y(t) = 0 and y"(t) + 2y(t) – 2x(t) = 37cos (3t). Find the trajectories x(t) and y(t).

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Q: 2: Find the orthogonal trajectories of xy=C.

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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.