In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y′′+2y′+y=6te−t+3t+9 with initial values
y(0)=2 and y′(0)=1.
(a) Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
(b) Write the fundamental solutions for the associated homogeneous equation.
(c) Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients.
(d) Write the general solution.
(e) Plug in the initial values and solve for c1 and c2 to find the solution to the initial value problem.