We consider the non-homogeneous problem y" - y = 3 - 2x First we consider the homogeneous problem y" - y = 0: 1) the auxiliary equation is ar² + br + c = = 0. 2) The roots of the auxiliary equation are (enter answers as a comma separated list). 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution Ye = C₁Y1 + C₂y2 for arbitrary constants c₁ and C₂. Next we seek a particular solution y, of the non-homogeneous problem y" - y = 3 - 2x using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find y₂ =
We then find the general solution as a sum of the complementary solution Yc = C₁Y₁ + C22 and a particular solution: y = y + yp. Finally you are asked to use the general solution to solve an IVP. 5) Given the initial conditions y(0) = −1 and y (0) = 0 find the unique solution to the IVP y =