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Let u(t) and v(t) be linearly independent solutions of the second order DE a(t)y" + b(t)y' + c(t)y = 0. Assume that u(t) = u(t₁) = 0 and u(t)>0 for all t between to and t₁. Prove that v(t) = 0 for some t between to and t₁. SUGGESTION: Wronskian.

Let u(t) and v(t) be linearly independent solutions of the second order DE a(t)y" + b(t)y' + c(t)y = 0. Assume that u(t) = u(t₁) = 0 and u(t)>0 for all t between to and t₁. Prove that v(t) = 0 for some t between to and t₁. SUGGESTION: Wronskian.

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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Let u(t) and v(t) be linearly independent solutions of the second order DE a(t)y" + b(t)y' + c(t)y = 0. Assume that u(t) = u(t₁) = 0 and u(t)>0 for all t between to and t₁. Prove that v(t) = 0 for some t between to and t₁. SUGGESTION: Wronskian.
Transcribed Image Text:Let u(t) and v(t) be linearly independent solutions of the second order DE a(t)y" + b(t)y' + c(t)y = 0. Assume that u(t) = u(t₁) = 0 and u(t)>0 for all t between to and t₁. Prove that v(t) = 0 for some t between to and t₁. SUGGESTION: Wronskian.
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