Find the general solution of the differential equation y" + y = 14 sin(2t) + 8t cos(2t).

Question

Find the general solution of the differential equation

y" + y = 14 sin(2t) + 8t cos(2t).

NOTE: Express the general solution in the form c₁y₁(t) + c₂y₂(t) + y_p(t), where c₁, c₂ are arbitrary constants and y_p(t) is the particular solution.

The general solution is: y(t)=

Answer 1

First: find the characteristic solution ... r²+1=0 thus r=±j, imaginary roots thus the so y_c= Asint+Bcost. Next find the particular solution recognizing that it's form y_p= Csin(2t)+Dtcos(2t)+Etsin(2t)

Substitute the yp & y_p'' into the original problem and evaluate the constants C, D,&E