7. (15pts) Consider the two-point boundary value problemu" + 2xu' x²u = x², u(0) = 1, u(1) = 0.-(a) Let h=1/4. Write out the difference equations explicitely, usingcentered-difference quotients for all derivatives.(b) Convert the equations to a linear system Ax = b, and then solve the system(either by hand or using MATLAB).

Answered: 7. (15pts) Consider the two-point…

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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Similar questions

Find two linearly independent solutions of 2x²y" - xy' + (-1x + 1)y = 0, x > 0 of the form Y₁ = x¹(1+ a₁x + ª²x² + α3x³ +.. ...). Y₂ = x¹(1+b₁x + b₂x² + b3x³ + ...) where r₁ > T2. Enter r1 = a₁ = a2 az = 12 b₁ = b₂ b3 = =
Find the nonhomogeneous ODE whose general solution is y=c₁(x+1)+c₂(x+1)³+x−1 . (x + 1)² y" + (x + 1) y' - 9y = 10 - 8x (x + 1)² y" + (x + 1) y' - 9y = - 8x (x² +1) y" +(²+1) y' - 9y = 10 - 8x (²+1) y" + (x + 1) y - 9y = - 8x D. (x + 1)² y" + (x + 1) y' - 9y = x - 1 E. (x² + 1) y" + (x² +1) y' - 9y = x - 1 F. G. None of the choices B. C.
4. (a) find and solve the indicial equation, (b) determine the appropriate form of each of the two linearly independent solution (c) find the first five nonzero terms of the two linearly independent solutions. (i) (ii) xy" + (1-x) y' + y = 0 x(x-1) y" + 3y' -2y = 0 5. Find only the form that the two linearly independent solution should take (i) 25x(1-x²) y" - 20(5x-2)y' + (25x- 4/x)y = 0
Solve the following system : x'₁ (t) = −x₁ (t) + 2x2(t) + 2x3 (t) − 2 x' (t) = 2x₁ (t) + 2x2 (t) + 4x3 (t) x' (t) = 2x₁1 (t) + 4x2 (t) + 2x3 (t) + 1.
Classify the equilibrium points (as sink, sources, or saddles) for the system sin x2 X1 + x2 sin x1 x2 X1 + x2 also, sketch the phase portrait.
Vo O Question The general series solution near the ordinary point x = 0 of the following differential equation (x2 – 4)y" + 3xy' +y = 0 is:
true or false
The values of C₁ and C₂ so that y(x) = C₁x + C₂ (-¹) satisfies 3x the two conditions y(1) = 1 and y'(1) = -1 are: O C1=1 and C2=0 O C1=1/3 and C2=2 O C1=1/3 and C2=-2 O C1-5/3 and C2=2
Explain in detail please
true or false
7. Express the general solution to the following system in terms of real- 30-2 -1 1 0 210 valued functions: x': = 8³] X.
Please find all the equilibrium points in the autonomous system. Please show work clearly I have trouble reading jumbled numbers. Thank you.

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