Solving Non-Homogeneous DE - Undermined Coefficients Consider " Order nonhomogeneous linear equation Ly = g(x) Where Ly = av "+a,_y(" -D+...+ay"tay'tay 1. Solve the associated homogeneous equation LV = 0 2. Assume a particular solutoin corresponding to (2) a. For a polynomial of degree ", assune a polynomial of degree " . b.. For term like " , assume a Yp = Ae C. For terms like sin BX e cos Bx assume Vp = Ae cos Bx+ Be sin Bx d. For multiple root with multiplicity ", multiply these assumed terms by X 3. Write the assumed form for the particular solution and evaluate the undermined coefficients. 4. Write the general solution "(X) =V. (x) + v.(x)Solving Second-order Non-homogenous DE using Undermined Coefficients method. (20 points) Consider the second-order non-homogeneous DE, V"+2v'-3y =7+ 3e-3x. a. (5 pts) Solve the associated homogeneous equation and find the complimentary solution .(xx) y. (x) = b. (6 pts) Write (), S, and " , then write the appropriate assumed form for the particulate solution V () with undermined coefficients that you learned in class. g(x) = S= m = V, (X) = c. (8 pts) Find the particular solution . of the above DE. d . (1 pt) Write the general solution of the above DE