dy dy + 12y = 0, (y(t) is the position at time t) dt2 dt (i) Rewrite the given second order differential equation as a system of first order differential equations for an unknown vector function Y() = ( ). y(t) v(t) (v(t) is the velocity at time t) (ii) Find two nonzero solutions of the differential equation that are not multiples of one another by seeking them in the form y(t) = est (iii) Use (ii) to find both straight line vector solutions of the system in (i)

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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.