Solving Non-Homogeneous DE - Variation of Parameters Second-order nonhomogeneous linear equation ay"tay'tay = g(x) Step 1: Find the complementary solution " (x) y.(x)=GM(x)+czy.(x>) Step 2: Write VP(x) using variation of parameters (X) = ()(x)+V,(x)y, (x) Step 3: Write the condition on the derivatives, and V/2 MityV =g(x) a2 Step 4: Solve the above system of two equations for V's and 12 . Step 5: Integrate 1 and /2 to find Vi and 12 Vi(x) = [Vi(x>dx and V, (x) = [V, (x)dx step 6: Write the particular solution JP as "'s()=1()(x)+12(9)>,(x) Step 6: Write the general solution V= Ve typSolving Second-order Non-homogeneous DE using Variation of Parameters method. v"+ 3y'+ 2y=- (20 points) Consider the second-order non-homogeneous DE, a. (5 pts) Solve the associated homogeneous equation and find the complimentary solution .() b. (2 pt) Write the appropriate form for the particulate solution V(x) with unkonwn functions 1() and V2(x) for Variation of Parameters method. c. (2 pts) Write the system of equations for 1(* and 1 V2(x) in order to solve Vi( x) and 2(x) d. (4 pts) Solve the above system for 1(x) and V2 (x ) e. (5 pts) Find 1(2) and 21) by integrating Vi(2) and Vi( x ) f. (1 pts) Using the above results and write the particular solution () of the DE. g. (1 pts) Finally, write the general solution of the above DE