Hello aspirant.

By converting D operator, the equation will be

(D^2+1)y=cosx-sinx

The complementary equation:

D^2+1=0

D=+j,-j

y(cf)=Aexp(jx)+Bexp(-jx)

y(cf)=Csin(x+a),c and a are constant

y(pI)=1/(D^2+1)*(cosx-sinx)

y(pI)=x*1/2D*(cosx-sinx)

y(pI)=x/2*integration(cosx-sinx)dx

y(pI)=x(sinx+cosx)/2

Complete solution:

y=y(cf)+y(PI)

y=Csin(x+a)+x(sinx+cosx)/2

Hope this will help you.