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h initial conditions 3₁ (0) 1, (0) = 0. d the function y2 of t which is the solution of h initial conditions 32 (0) = 0, ₂(0) = 1. d the Wronskian 36y" +84y15y = 0 36y" +84y15y = 0 W(t) = W(y1, y2). (t) = mark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so y₁ and y2 form a fundamental set of utions of 36y" +84y - 15y = 0.

h initial conditions 3₁ (0) 1, (0) = 0. d the function y2 of t which is the solution of h initial conditions 32 (0) = 0, ₂(0) = 1. d the Wronskian 36y" +84y15y = 0 36y" +84y15y = 0 W(t) = W(y1, y2). (t) = mark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so y₁ and y2 form a fundamental set of utions of 36y" +84y - 15y = 0.

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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Find the function y₁ of t which is the solution of with initial conditions y₁ (0) = 1, ₁ (0) = 0. Y1 = Find the function y2 of t which is the solution of with initial conditions y2 (0) = 0, y(0) = 1. Y2 = Find the Wronskian 36y" +84y - 15y = 0 36y" +84y - 15y = 0 W(t) = = W (y1, y2). W(t) Remark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so y₁ and y₂ form a fundamental set of solutions of 36y" +84y - 15y = 0.
Transcribed Image Text:Find the function y₁ of t which is the solution of with initial conditions y₁ (0) = 1, ₁ (0) = 0. Y1 = Find the function y2 of t which is the solution of with initial conditions y2 (0) = 0, y(0) = 1. Y2 = Find the Wronskian 36y" +84y - 15y = 0 36y" +84y - 15y = 0 W(t) = = W (y1, y2). W(t) Remark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so y₁ and y₂ form a fundamental set of solutions of 36y" +84y - 15y = 0.
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