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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

Problem 44E

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