Q1: Apply the power series method to find the solution of the followingequationdifferential(1- x)y" + y = 0[1A = 2 43 4.Q2: Consider11a) Check if the A has LU decompositionb) Find an LU decompositionc) Then solveX1 + 2x2 + 3x32x1 + 4x2 + 5x3 = 6X1 + 3x2 + 4x3 = 2= 4Q3: a) Find the Z-transform forf(k) = k ek aQ3: b) Consider the function f (x)evaluate a root of this function, take xo = 0.48 as our first approximation.= tan(nx) – x – 6. Use the Newton method toNote: (solve the equation for six iterations by taking five decimal digit)

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Math

Advanced Math

Q1: Apply the power series method to find the solution of the following equation differential (1- x)y" + y = 0

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Q1: Apply the power series method to find the solution of the following
equation
differential
(1- x)y" + y = 0
[1
A = 2 4
3 4.
Q2: Consider
11
a) Check if the A has LU decomposition
b) Find an LU decomposition
c) Then solve
X1 + 2x2 + 3x3
2x1 + 4x2 + 5x3 = 6
X1 + 3x2 + 4x3 = 2
= 4
Q3: a) Find the Z-transform for
f(k) = k ek a
Q3: b) Consider the function f (x)
evaluate a root of this function, take xo = 0.48 as our first approximation.
= tan(nx) – x – 6. Use the Newton method to
Note: (solve the equation for six iterations by taking five decimal digit)

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