MATH 240 Final: Kansas State MATH 240 Math 240FinalU15

HW8: Problem 10 Previous Problem List | Next (1 point) We consider the non-homogeneous problem y"-4y, + 4y = 16x2 First we consider the homogeneous problem y"-4y + 4y = 0 : 1) the auxiliary equation is ar2 + br + c = 2) The roots of the auxiliary equation are 3) A fundamental set of solutions is complementary solution ye = ciyi + c2y2 for arbitrary constants q and c2 (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the problem y"-4y, + 4y = 16x2 using the rmethod of Next we seek a particular solution y, of the non-homogeneous undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find y, We then find the general solution as a sum of the complementary solution y cyi +022 and a particular solution: y=ye +y,"Finally you are asked to use the general solution to solve an IVP 5) Given the initial conditions y(0) = 8 and y(0) 14 find the unique solution to the IVP 26

Using Lagrange Multipliers In Exercises 1-8, use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. 1. Maximize: fa. y) - xy 2. Minimize: f(x,y) # 2x+) 3. Minimize f(x, y)-xy 4. Maximize f(x, y) 2-y 5. Maximize f(x, y) - 2x +2ry +y 6. Minimize /tx, y) -3x +y + 10 7. Maximize/(x,y)-V6-x-yi 8. Minimize/ky) Constraint: x+y 10 Constraint: ry 32 Constraint: x+2y 5-0 Constraint: 2y x2-0 Constraint: 2x + y Constraint: xy 6 Constraint: x +y 2 0 Constraint: 2x + 4y - 15 -0 100