QUESTION

Show that the solution to the initial value problem mu'' + gu' + ku = 0, u(t 0 )=u 0 , u'(t 0 )=u' 0 can be expressed as the sum u = v + w, where v

Show that the solution to the initial value problem mu’’ + gu’ + ku = 0, u(t0)=u0, u’(t0)=u’0 can be expressed as the sum u = v + w, where v satisfies the initial conditions v(t0) = u0, v’(t0) = 0, w satisfies the initial conditions w(t0) = 0, w’(t0) = u’0, and both v and w satisfy the same differential equation as u.  This is another instance of superposing solutions of simpler problems to obtain the solution of a more general problem.