These are the solutions to the problems, can you please show me the steps to reach these solutions? Thank you so much! (2) Assume xi(t)(i=1,2,3,,N) is a particular solution of a second-order non-homogeneous linear differential equation a2dt2d2x+a1dtdx+a0x=fi(t), Prove that i=1Nxi(t) is a particular solution of the equation a2dt2d2x+a1dtdx+a0x=i=1Nfi(t) (i) xj(t) is a particular solution of a second-order non-homogeneous linear differential equation a2dt2d2x+a1dtdx+a0x=fj(t); then, according to (1), g=i=12xi(t) is a particular solution of equation a2dt2d2x+a1dtdx+a0x=i=12fi(t) (ii) Let g=i=12xi(t)+x3(t), according to (1), g=i=13xi(t) is a particular solution of equation a2dt2d2x+a1dtdx+a0x=i=12fi(t)+f3(t)=i=13fi(t) (iii) accordingly, g=i=1r1xi(t)+xr(t) is a particular solution of equation a2dt2d2x+a1dtdx+a0x=i=1r1fi(t)+fr(t)=i=1rfi(t). (iv) let r=N, proof is completed