The general solution of Y '' - y = SiNx

The general solution of Y '' - y = SiNx

The characteristic equation of the homogeneous equation y '' - y = 0 is R & # 178; - 1 = 0, then r = ± 1
The general solution of the homogeneous equation y '' - y = 0 is y = C1E ^ t + c2e ^ (- t) (C1, C2 are integral constants)
Let a solution of the original equation be y = asinx + bcosx
Substituting into the original equation, - 2asinx-2bcosx = SiNx
==>-2A=1,-2B=0
==>A=-1/2,B=0
A solution of the original equation is y = - SiNx / 2
So the general solution of the original equation is y = C1E ^ t + c2e ^ (- t) - SiNx / 2 (C1, C2 are integral constants)