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Suppose the characteristic equation of a second-order Cauchy-Euler equation has a repeated root r = CER. (a) What's one solution of this ODE? Call this y₁. (b) To find a second solution that is linearly independent from the first, suppose y2 = u - y1, where u = u(r). Solve for u(r) and then find y2(2). (c) Show that y₁ and y2 are indeed linearly independent.

Suppose the characteristic equation of a second-order Cauchy-Euler equation has a repeated root r = CER. (a) What's one solution of this ODE? Call this y₁. (b) To find a second solution that is linearly independent from the first, suppose y2 = u - y1, where u = u(r). Solve for u(r) and then find y2(2). (c) Show that y₁ and y2 are indeed linearly independent.

Advanced Engineering Mathematics
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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4. Suppose the characteristic equation of a second-order Cauchy-Euler equation has a repeated root r = c E R. (a) What's one solution of this ODE? Call this y₁. (b) To find a second solution that is linearly independent from the first, suppose y2 = u - Y1, where u = u(x). Solve for u(x) and then find y2(x). (c) Show that y₁ and y2 are indeed linearly independent.
Transcribed Image Text:4. Suppose the characteristic equation of a second-order Cauchy-Euler equation has a repeated root r = c E R. (a) What's one solution of this ODE? Call this y₁. (b) To find a second solution that is linearly independent from the first, suppose y2 = u - Y1, where u = u(x). Solve for u(x) and then find y2(x). (c) Show that y₁ and y2 are indeed linearly independent.
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