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Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³ and 2 = ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the solutions are linearly independent. Wronskian = det | These solutions are linearly independent because the Wronskian is Choose for all x.

Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³ and 2 = ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the solutions are linearly independent. Wronskian = det | These solutions are linearly independent because the Wronskian is Choose for all x.

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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please solve both 2 parts

,3x Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³x and ze ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the solutions are linearly independent. Wronskian = det TE These solutions are linearly independent because the Wronskian is Choose ✓for all x.
Transcribed Image Text:,3x Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³x and ze ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the solutions are linearly independent. Wronskian = det TE These solutions are linearly independent because the Wronskian is Choose ✓for all x.
Use the Wronskian to determine whether the functions y₁ = Wronskian = det [ sin(2x) and y2 = cos(6x) are linearly independent. ] = These functions are linearly independent because the Wronskian is nonzero for Choose value(s) of x.
Transcribed Image Text:Use the Wronskian to determine whether the functions y₁ = Wronskian = det [ sin(2x) and y2 = cos(6x) are linearly independent. ] = These functions are linearly independent because the Wronskian is nonzero for Choose value(s) of x.
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