A. Given below are particular solutions ??. Determine the (a) roots of the characteristic equation for a homogeneous linear equation with real constant coefficients and (b) its general solution. 1. y=x(e2x+4)2. y = x2sinx + xcosx3. y=8cos4x+sin3x4. y=x2-x+e-x(x+cosx)5. y=cos2x B. Obtain the following:a.) the characteristic roots ? of the system b.) the roots ?′ of the input c.) the general solution ? using undetermined coefficients1. y"-y=8xex2. y"-3y'-4y+30e4x3. y"+y=cosx4. y"-y'-2y=6x+6e-x

Given: 1) y=x(e2x+4) e2x is initiated by D-2 [D-2] e2x = 2 e2x-e2x=0 so , x e2x is annihilated…

Answered: . Obtain the following: a.) the…

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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A. Given below are particular solutions ??. Determine the (a) roots of the characteristic equation for a homogeneous linear equation with real constant coefficients and (b) its general solution.

1. y=x(e^2x+4)

2. y = x²sinx + xcosx

3. y=8cos4x+sin3x

4. y=x²-x+e^-x(x+cosx)

5. y=cos²x

B. Obtain the following:
a.) the characteristic roots ? of the system
b.) the roots ?′ of the input
c.) the general solution ? using undetermined coefficients

1. y"-y=8xe^x

2. y"-3y'-4y+30e^4x

3. y"+y=cosx

4. y"-y'-2y=6x+6e^-x

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