Find the function y₁ of t which is the solution of with initial conditions y₁ (0) 1, (0) = 0. -0 y1 = Find the function y₂ of t which is the solution of with initial conditions y2 (0) = 0, y/₂(0) = 1. Y2 = Find the Wronskian 9y" - 81y = 0 9y" - 81y = 0 = W (y1, y2). W(t) = (Hint: write y₁ and y2 in terms of hyperbolic sine and cosine and use properties of the hyperbolic functions). W(t) = Remark: You should find that W is not zero and so y₁ and y₂ form a fundamental set of solutions of 9y" - 81y = 0.
Find the function y₁ of t which is the solution of with initial conditions y₁ (0) 1, (0) = 0. -0 y1 = Find the function y₂ of t which is the solution of with initial conditions y2 (0) = 0, y/₂(0) = 1. Y2 = Find the Wronskian 9y" - 81y = 0 9y" - 81y = 0 = W (y1, y2). W(t) = (Hint: write y₁ and y2 in terms of hyperbolic sine and cosine and use properties of the hyperbolic functions). W(t) = Remark: You should find that W is not zero and so y₁ and y₂ form a fundamental set of solutions of 9y" - 81y = 0.
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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