Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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