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√2 1. Verify that y₁(x) = e-x/³ COS x and y₂ (x): 3 = e-x/3 sin- x are solutions of the differential equation 3 3y" + 2y + y = 0 on (-∞, ∞) Compute the Wronskian W (y1, y2) and determine if {y₁, y₂} forms a fundamental set of solutions.

√2 1. Verify that y₁(x) = e-x/³ COS x and y₂ (x): 3 = e-x/3 sin- x are solutions of the differential equation 3 3y" + 2y + y = 0 on (-∞, ∞) Compute the Wronskian W (y1, y2) and determine if {y₁, y₂} forms a fundamental set of solutions.

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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√2 1. Verify that y₁(x) = e¯x/³ cos- x and y₂ (x) = e-x/³ sin x are solutions of the differential equation 3 3 3y" + 2y' + y = 0 on (-∞, ∞) Compute the Wronskian W (y1, y2) and determine if {y₁, y₂} forms a fundamental set of solutions.
Transcribed Image Text:√2 1. Verify that y₁(x) = e¯x/³ cos- x and y₂ (x) = e-x/³ sin x are solutions of the differential equation 3 3 3y" + 2y' + y = 0 on (-∞, ∞) Compute the Wronskian W (y1, y2) and determine if {y₁, y₂} forms a fundamental set of solutions.
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