The differential operator D2- 8D+80 has the form D2- 2aD +a² + B? where a = and B= Therefore D - 8D + 80 should annihilate the functionf= e cos(8r) and g= et sin(8r). We will check that for et cos(8z). Note that when we compute the derivative and second derivative we will get terms that have ez sin(8z) in them, so we will have to account for them below. Compute D2 (ez cos(8z)), -8D(e cos(8z)), and 80e cos(8z). Place the coefficients from the terms etz cos(8z) and e sin(8r) in the table. The columns of the table should add to zero.

The differential operator D2- 8D+80 has the form D2- 2aD +a² + B? where a = and B= Therefore D - 8D + 80 should annihilate the functionf= e cos(8r) and g= et sin(8r). We will check that for et cos(8z). Note that when we compute the derivative and second derivative we will get terms that have ez sin(8z) in them, so we will have to account for them below. Compute D2 (ez cos(8z)), -8D(e cos(8z)), and 80e cos(8z). Place the coefficients from the terms etz cos(8z) and e sin(8r) in the table. The columns of the table should add to zero.

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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