8. (1) Assume x, (t) is a particular solution of a second-order non-homogeneous linear differential d'x dx equation a2 dt- + al +dox= fi(t) , and x2 (t) is a particular solution of the equation dt d'x dx az + a +dox= f(t) . Prove that x, (t)+x, (t) is a particular solution of the equation dt dt d' x dx a + a, tax=f,(t)+ f(t) . Note that the three differential equations have the same dt2 dt coefficients a2, al and do. (2) Assume x. (t) (i=1,2,3,..., M) is a particular solution of a second-order non-homogeneous linear d' x dx differential equation a2 + a1 + do x = fi(t), Prove that Ex, (t) is a particular solution of the dt2 dt i=1 d' x dx N equation a2 dt2 + al tax = Ef. (t). dt i=1