Given the boundary value problema*y" – xy' + y = In rwith the conditionsy(1) = 0, y(2) = -2.%3D(a) Using finite difference method, show that the difference equation for the above problem can bewritten as(1+)m+ (-2+)»+ (1-2).. -hYi-1hYi+12.x;Yiwhere h = Ar.(b) Using equation in part (a) and the boundary conditions, obtain a linear system in the formAy = b, where h = 0.2.(c) Write the Gauss Seidel formula for the above system Ay = b found in part (b).(DO NOT SOLVE the system)%3D

Given, the boundary value problem x2y''-xy'+y=lnx ...(1) with the…

Answered: Given the boundary value problem

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider a fuel distribution center located at the origin of the rectangular coordinate system (units in miles; see figures). The center supplies three factories with coordinates (4, 1), (5, 6), and (10, 3). A trunk line will run from the distribution center along the line y = mx, and feeder lines will run to the three factories. The objective is to find m such that the lengths of the feeder lines are minimized. Minimize the sum of the lengths of the perpendicular feeder lines from the trunk line to the factories given by as attached. Find the equation of the trunk line by this method and then determine the sum of the lengths of the feeder lines.
2. In submarine location problems, it is often important to find a submarine's closest point of approach to a sonobuoy (a sound detector). Suppose that a submarine travels along a parabolic path y = x² and the sonobuoy is at position (2, -0.5). It has been known that the value of a needed to minimize the distance between the submarine and the buoy must satisfy the following equation 1 1+x² 1 x= Use Newton's Method to find a solution to the equation x = 9 decimal places. 1 1+x² correct up to
Consider the following linear programing problem: P = 2x + 3y subject to 2x + 5y ≤ 20 Resource 1 3x + 2y ≤ 17 Resource 2 as well as x ≥ 0 and y ≥ 0. Use the method of corners (showing your graph and corner points) to solve this problem. (i.e. Find the number of x and y so that P is optimized) Hint: If you are dealing with a bounded area, then it is a maximizing problem. Will the optimal solution you found in part “a” remain optimal if coefficient of x changes to 1 in the “objective function”? How do you know? What is the range of values for the coefficient of x in the objective function to keep the optimal solution unchanged? Will the solution remain optimal is amount of Resource 2 changes to 20? How do you know?
Two-Point BVPs. In each of Problems 1 through 12, either solve the given boundary value problem or else show that it has no solution:
find the minimum value of z = 4x + 5y, subject to the following constraints: 2x+y≤6; x≥0; y ≥0; x+y≤5. give a vertex of the region along the y - axis .
4) Consider the following LP Minimize Subject to Z = 5X₁ + X2, 2x1 + x2 ≥ 6 x1 + x2 ≥ 4 2x+10x2 ≥ 20 and X₁ ≥ 0, x₂ ≥0. Use the graphical method to solve this problem. Solve for the value of each corner point feasible solution as well as the optimal answer.
Maximize R = 2x + 3ySubject to:2x – y <= 10 (constraint 1)x + 3y <= 6 (constraint 2)x,y ≥ 0 1. Does the graph of constraint 1 pass through (0,0)? 2. Does the graph of constraint 2 pass through (1,1)? 3. How many corner points can be identified from the graph of LP model? 4. What values of x and y will maximize R? 5. What is the maximized value of R?
Let f(x, y) = xy² and r(t) = (¹/1²,t³). Calculate Vf. (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) Vf= Calculate r' (t). (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) r' (t) = Use the Chain Rule for Paths to evaluateƒ(r(t)) at t = 1.5. (Use decimal notation. Give your answer to three decimal places.) d dt - ƒ(r(1.5)) = = Use the Chain Rule for Paths to evaluate ƒ(r(t)) at t = -1.7. (Use decimal notation. Give your answer to three decimal places.) d dt d f(r(-1.7)) =

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