let L=D^3 +D +x be a differential operator and y1(x)=sin(x), y2(x)=x. Verify that L(y1)=xsinx and L(y2)=x^2 +1. what is the particular solution of the following equations?(use the superposition principle)a)L[y]=2xsin(x)-x^2-1 b)L[y]= 4x^2 +4 - 6xsin(x) 2. Let L = D3 + D+ x be a differential operator and y1(x) = sin(x), Y2(x) = x. Verify thatL(y1) = x sin(x) and L(y2) = x² + 1. Use the superposition principle to find a particular solutionto the equations(a)L[y] = 2x sin(x) – x² – 1, (b)L[y] = 4x? + 4 – 6x sin(x).

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Answered: 2. Let L = D3 + D+ x be a differential…

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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let L=D^3 +D +x be a differential operator and y1(x)=sin(x), y2(x)=x. Verify that L(y1)=xsinx and L(y2)=x^2 +1. what is the particular solution of the following equations?(use the superposition principle)

a)L[y]=2xsin(x)-x^2-1

b)L[y]= 4x^2 +4 - 6xsin(x)

2. Let L = D3 + D+ x be a differential operator and y1(x) = sin(x), Y2(x) = x. Verify that
L(y1) = x sin(x) and L(y2) = x² + 1. Use the superposition principle to find a particular solution
to the equations
(a)
L[y] = 2x sin(x) – x² – 1, (b)
L[y] = 4x? + 4 – 6x sin(x).

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