Write the given second order equation as its equivalent system of first order equations. u" – 7.5u' + 1.5u = -3 sin(3t), u(1) = 0, u'(1) = = 1.5 Use v to represent the "velocity function", i.e. v = u'(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) Now write the system using matrices: :三一 u dt V and the initial value for the vector valued function is: v(1)

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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.