Please show the solutions to how it arrived to the answers. Thank you!!!

Solve the following differential equations. 4. y""' - 7y" + 14y' - By = 0 Ans: y = Ge* + Cze2* + Cze* 5. (DS - 11D* + 19D3 + 115D= - 200D - 500)y = 0 Ans: v= Ce-=" + Caxe-2" + Cag5* + Coxes* + Coxlex 6. (D + 3D* + 3D= + 1)y = 0 Ans: y = C cosx + Coxcosx+ Cax'cosx + C, sinx+ Cox sinx + Cox sinx 7. y"ty'ty=0 Ans: y = e (Ci cos , x + C, sin -X