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Consider the following system of differential equations 3x + y = 0, dy 20x+6y= 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (²) = C₁ (1₁) e^² + (₁₁) eat Y2 where C₁ and C₂ are constants. Give the values of A1, 91, A2 and y2. Enter your values such that A₁ < ₂. A₁ = Y1 = A₂ = Y2 = Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as a (t) and y(t), which satisfies the initial conditions (0) = 5, y(0) = 22. x(t) = y(t) da dt eit C₂

Consider the following system of differential equations 3x + y = 0, dy 20x+6y= 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (²) = C₁ (1₁) e^² + (₁₁) eat Y2 where C₁ and C₂ are constants. Give the values of A1, 91, A2 and y2. Enter your values such that A₁ < ₂. A₁ = Y1 = A₂ = Y2 = Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as a (t) and y(t), which satisfies the initial conditions (0) = 5, y(0) = 22. x(t) = y(t) da dt eit C₂

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 65E
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Consider the following system of differential equations 3x + y = 0, dy 20x+6y=0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (1) - (1) (1) * = C₁ edit + C₂ where C₁ and C2 are constants. Give the values of A1, y1, A2 and y2. Enter your values such that A₁ < ₂. A₁ = Y1 = 12: = Y2 = Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as x (t) and y(t), which satisfies the initial conditions (0) = 5, y(0) = 22. x(t) = y(t) = da dt
Transcribed Image Text:Consider the following system of differential equations 3x + y = 0, dy 20x+6y=0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (1) - (1) (1) * = C₁ edit + C₂ where C₁ and C2 are constants. Give the values of A1, y1, A2 and y2. Enter your values such that A₁ < ₂. A₁ = Y1 = 12: = Y2 = Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as x (t) and y(t), which satisfies the initial conditions (0) = 5, y(0) = 22. x(t) = y(t) = da dt
Consider the following system of differential equations +x+y=0, dy 8x + 7y=0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form ( * ) - 0₁ (1) ²² + 0₂ (1) ² = edit Y where C₁ and C2 are constants. Give the values of A1, Y₁, A2 and y2. Enter your values such that X₁ < ₂. X₁ - Yı = X₂ = Y2 Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as x(t) and y(t), which satisfies the initial conditions x (0) = 4, y(0) = 14. X x(t) = y(t) = dx dt -
Transcribed Image Text:Consider the following system of differential equations +x+y=0, dy 8x + 7y=0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form ( * ) - 0₁ (1) ²² + 0₂ (1) ² = edit Y where C₁ and C2 are constants. Give the values of A1, Y₁, A2 and y2. Enter your values such that X₁ < ₂. X₁ - Yı = X₂ = Y2 Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as x(t) and y(t), which satisfies the initial conditions x (0) = 4, y(0) = 14. X x(t) = y(t) = dx dt -
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