(1 point) We consider the non-homogeneous problem y" + 4y + 5y = 65 sin(2x) First we consider the homogeneous problem y"

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1 Point We Consider The Non Homogeneous Problem Y 4y 5y 65 Sin 2x First We Consider The Homogeneous Problem Y 1 (90.31 KiB) Viewed 85 times

(1 point) We consider the non-homogeneous problem y" + 4y + 5y = 65 sin(2x) First we consider the homogeneous problem y" + 4y' + 5y = 0: 1) the auxiliary equation is ar² + br+c= r^2+4r+5 2) The roots of the auxiliary equation are -2+i,-2-i 3) A fundamental set of solutions is e^(-2x)cosx,e^(-2x)sinx C2. = 0. (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = c₁y₁ + c₂y₂ for arbitrary constants ₁ and Next we seek a particular solution y of the non-homogeneous problem y" + 4y' + 5y = 65 sin(2x) using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find yp We then find the general solution as a sum of the complementary solution yc = C₁y₁ + c2y2 and a particular solution: y = yc + Yp. Finally you are asked to use the general solution to solve an IVP. 5) Given the initial conditions y(0) = -9 and y' (0) = 2 find the unique solution to the IVP y =