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Consider the following system of differential equations +22+1=0, dy - 4y = 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form ( ₁ ) = C₁ ( 1 ) ex² + 0₂ (1) ebe eht et where C₁ and C₂ are constants. Give the values of A1, 31, A2 and y2. Enter your values such that A₁ < ₂. A₁ = 3₁ = A₂ = y2 = Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as 2 (t) and y(t), which satisfies the initial conditions z(0) = 3, y(0-12. r(t) = y(t) = da dt

Consider the following system of differential equations +22+1=0, dy - 4y = 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form ( ₁ ) = C₁ ( 1 ) ex² + 0₂ (1) ebe eht et where C₁ and C₂ are constants. Give the values of A1, 31, A2 and y2. Enter your values such that A₁ < ₂. A₁ = 3₁ = A₂ = y2 = Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as 2 (t) and y(t), which satisfies the initial conditions z(0) = 3, y(0-12. r(t) = y(t) = da dt

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 +22+1=0, dy - 4y= 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form I ( ₁ ) = C₁₂ (₁1₁) er ² a et + C₂ (1₂) elat 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 = 32= 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) = 3, y(0-12. ข(0)= r(t) = y(t) = da dt
Transcribed Image Text:Consider the following system of differential equations +22+1=0, dy - 4y= 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form I ( ₁ ) = C₁₂ (₁1₁) er ² a et + C₂ (1₂) elat 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 = 32= 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) = 3, y(0-12. ข(0)= r(t) = y(t) = da dt
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