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6. Complex trigonometric functions, ODE and independence 3π a) Find the real part of following expression: cos -+12y-cos 37 - 12y 8 8 b) A second order ODE has basis y₁ = cos Ax and y₂ = sin Ax where A is a non-zero constant. i) Identify its eigenvalues and type of damping. ii) Show if these functions are independent with Wronskian. c) A second order ODE has basis y₁=e³x cos 3x and y₂ = ³x sin 3x where B is a constant. i) Identify its eigenvalues and the case of its general solution. -Bx e-Bx ii) Find the ODE.

6. Complex trigonometric functions, ODE and independence 3π a) Find the real part of following expression: cos -+12y-cos 37 - 12y 8 8 b) A second order ODE has basis y₁ = cos Ax and y₂ = sin Ax where A is a non-zero constant. i) Identify its eigenvalues and type of damping. ii) Show if these functions are independent with Wronskian. c) A second order ODE has basis y₁=e³x cos 3x and y₂ = ³x sin 3x where B is a constant. i) Identify its eigenvalues and the case of its general solution. -Bx e-Bx ii) Find the ODE.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 35EQ
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6. Complex trigonometric functions, ODE and independence ( 3πT a) Find the real part of following expression: cos +12y-cos 8 8 b) A second order ODE has basis y₁ = cos Ax and y₂ = sin Ax where A is a non-zero constant. i) Identify its eigenvalues and type of damping. ii) Show if these functions are independent with Wronskian. c) A second order ODE has basis y₁ = ³x cos 3x and y₂ = e¯³x sin 3x where B is a constant. i) Identify its eigenvalues and the case of its general solution. ii) Find the ODE.
Transcribed Image Text:6. Complex trigonometric functions, ODE and independence ( 3πT a) Find the real part of following expression: cos +12y-cos 8 8 b) A second order ODE has basis y₁ = cos Ax and y₂ = sin Ax where A is a non-zero constant. i) Identify its eigenvalues and type of damping. ii) Show if these functions are independent with Wronskian. c) A second order ODE has basis y₁ = ³x cos 3x and y₂ = e¯³x sin 3x where B is a constant. i) Identify its eigenvalues and the case of its general solution. ii) Find the ODE.
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