Please help! I keep getting the problems wrong. Take your time and thank you for your help!

A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. 17 0"-40'-120=5-2t, 0 (t)= - + 36 6 17 The general solution is 0(1) = cq et + cze -2- 36 6 (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)Determine the form of a particular solution for the differential equation. Do not solve. y" -y=2ed + 6te 31 + 4+2 3t The form of a particular solution is y(t) = Get c, e -+ + 3t 2 (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)Determine the form of a particular solution for the differential equation. Do not solve. y" - 12y' + 36y =theft - e 6t 6t+ 2 The form of a particular solution is y (t) = c, et + cate 6t. 12 2 (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)Find a general solution to the differential equation using the method of variation of parameters. y" + 25y =2 sec 5t The general solution is y(t) = c, ev2 sec (5t) - 25t + Co e - V2 sec (5t) - 25tFind a general solution to the differential equation using the method of variation of parameters. y" + 25y =2 csc -5t 5t - 2 In tan cos (5t) - 2 The general solution is y(t) = c, cos (5t) + c, sin (5t) + 25