Consider the second order differential equation with initial conditions u" + 6u' - 2.5u = -6 sin(3t), u(1) = -8, u'(1) = -6.5. Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single letter u to represent the function u and the single letter v to represent the "velocity function" u'. Do not use u(t) or v(t) to represent these functions. Expressions like sin(t) that represent other functions are OK. 1 = Now write the first order system using matrices: dt The initial value of the vector valued solution for this system is: u(1) v(1 )