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Consider the following system of differential equations + x + y = 0, - 8x + 7y=0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (₁) = ₁₂ (¹) edit 0₂ (1) ekst where C₁ and C₂ are constants. Give the values of A1, 91, A2 and y2. Enter your values such that A₁ < A₂. X₁ - Y₁ = 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 (0) = 4, y(0) = 14. x(t) = y(t) = dx dt dy +

Consider the following system of differential equations + x + y = 0, - 8x + 7y=0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (₁) = ₁₂ (¹) edit 0₂ (1) ekst where C₁ and C₂ are constants. Give the values of A1, 91, A2 and y2. Enter your values such that A₁ < A₂. X₁ - Y₁ = 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 (0) = 4, y(0) = 14. x(t) = y(t) = dx dt dy +

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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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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