Answered: 22.5 Problem. Repeat the work above for… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 5T

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22.5 Problem. Repeat the work above for the transport IVP
U₁ + Ux = 0, −∞ <x, t< ∞
Ut
u(x, 0) = f(x), −x<x<∞
and recover the expected, beloved formula u(x,t) = f(x − t).
transform to u in x and get an ODE-type IVP for u. Solve it.
[Hint: apply the Fourier
Then recover u from its
Fourier transform via Untheorem 22.2. Do some algebra in the integrand and recognize the
integral as the Fourier transform of f.]
22.2 Untheorem. Let f: RC be "nice." Then
f(x) = √1/= Lº° ƒ(k)eik² dk.
2πT

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1.2 Find the general solution of dy -2x6 dr +y = y-4
2. (LI-2) Consider the equation r²y" - xy + y = 0. It is given that y₁ = z is one solution to this equation. Use reduction of order to find a second solution 92 which is linearly independent from y₁.
#1 Solve the following non-linear equations manually using: a) Bisection Method (5 iterations)
I already posted this problem but would like a more thorough explanation I am completely lost still.
Classify each of the equations above as separable, linear, exact, can be made exact, Bernoulli, Riccatti, homogeneous, linear combination, or neither. y′=x+√y; y′=x^2+y^2. y′=xy+√xy y′=1/x(x−y)
5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).
For the equation ay" + by' + cy = 0, if b² – 4ac = 0 (the repeated root case where the root is r = -b/2a) we learned that one solution is Y1 = e-bt/2a, and the second linearly independent solution is y, = te-bt/2a We were told that the second solution is found via the Reduction of Order method. Apply the Reduction of Order method to the equation using the first solution (Do the calculations, this will take about 5 or so minutes) Which of the following equations does it reduces to? au" + 2bu' - u + cu = 0 2a 62 àu" – 2bu' +u + cu = 0 au" = 0 au" + 2bu' + Eu + cu = 0 O O O
1. Solve for the unknown/s. 1. x: 4 = (2x + 3) = 12 2. (x + 1): (2x + 3) = (x + 3)(2x + 8) 3. (3x - 1): (3x + 1) = (x + 8): (x + 12) 4. (x + 2):3 - 2: (5 - x)
Solve 2æy" +(z+1)+y =0 using y=
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(12.1) SOLVE 30 KULTURT 2 x²y" + xy² + (1x² - 2) y = 0 BY BECIELS METHOD.
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