y"-3y +2y= 4te' - 3e-(2t +1) with initial values y(0) = 3 and y'(0) = 5. A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.) B. Write the...

In this problem you will use undetermined coefficient to solve the non homogeneous equation.

y"-3y'+2y=4te^t-3e^t-(2t+1)

Extracted text: y"-3y +2y= 4te' - 3e-(2t +1) with initial values y(0) = 3 and y'(0) = 5. 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. Y1 = Y2 = C. Write the form of the particular solution and its derivatives (Use A, B, C, etc. for undetermined coefficients. Y Y' = Y" = D. Write the general solution. (Use c1 and c2 for c1 and c2). E. Plug in the initial values and solve for c1 and c, to find the solution to the initial value problem. Hint: No fractions are required in the solution or answer to this problem.