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- Find a solution: ty''-ty'+y=2; y(0)=2,y'(0)=-17 b) For the system, 6 - 1 Y': Y 5 4 Write the natural period of the oscillations, round the answer to three digits after the decimal signWrite the given second order equation as its equivalent system of first order equations. u" + 4.5u' – 7.5u = -7 sin(3t), u(1) = -7.5, u'(1) = -6 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.) u' = %3D Now write the system using matrices: u d + dt V V and the initial value for the vector valued function is: u(1) v(1)