Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) v+ 2y' +2y =15t sint What is/are the root(s) of the auxiliary equation associated with the given differential equation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. () A. There are no roots to the associated auxiliary equation. ) B. The associated auxiliary equation has the two roots (Use a comma to separate answers as needed.) O . The associated auxiliary equation has the double root Write the form of a particular solution. Choose the correct answer below. Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) y" + 2y' + 2y = 15t e- sint . . . Write the form of a particular solution. Choose the correct answer below. O A. yp(t) =t(Agtu + Ant2 + Ant+ Ap) e"cost+t(Bat3 + Byt2 + Byt+Bo)e" sint O B. yp(t) =t(Agt + At2 + Ant+ Ap) e cost+t(Bat3 + Byt2 + Byt+ Bo)e sint O c. yp(1) = (Agt3 + A212 + Ant+ Ap)e cost+ (Bat3 + B212 + Byt+ Bo) e'sint O D. yp(1) = (Agt + At2 + Ant+ Ap)e"cost+ (Bat3 + Byt2 + Bit+Bo) e" sint