1) Find a particular solution to the differential equation using the Method of Undetermined Coefficients. x''(t) - 18x'(t) + 81x(t) = 3te^(9t)

2)The auxiliary equation for the given differential equation has complex roots. Find a general solution. 12y''-12y'+78y=0

3) Find a particular solution to the differential equation using the Method of Undetermined Coefficients. y'' + 9y' + 18y = (2050e^(2t))cos(10t)

4)A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation.

y'' + 10y' + 16y = 48x^2 + 60x + 6 + 27e^x, yp(x) = e^x + 3x^2

5)solve the given Initial value Problem

y''-3y'+2y=0, y(0) =1/2, y'(0)= -3/4