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2. Given the system dx₁ = 3x₁ + 3x₂ dt dx₁ dt = 4x₁ - 1x₂ a. Write the above system in matrix form ie =Ax. What is A ? dx dt b. Find et (Use the full process I showed in class, using the associated linear differential equation and finding its natural fundamental set of solutions associated to time t = 0. Then, do it again with the Two-by-Two Matrix Exponential Formulas in section 4.3 of book.) C. Give a general solution of the system. d. Give the solution of the IVP with initial value x(0) = e. Give the solution of the IVP with initial value x(1) = (3) using e¹A

2. Given the system dx₁ = 3x₁ + 3x₂ dt dx₁ dt = 4x₁ - 1x₂ a. Write the above system in matrix form ie =Ax. What is A ? dx dt b. Find et (Use the full process I showed in class, using the associated linear differential equation and finding its natural fundamental set of solutions associated to time t = 0. Then, do it again with the Two-by-Two Matrix Exponential Formulas in section 4.3 of book.) C. Give a general solution of the system. d. Give the solution of the IVP with initial value x(0) = e. Give the solution of the IVP with initial value x(1) = (3) using e¹A

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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2. Given the system dx₁ dt dx dt C. = 3x₂ + 3x₂ -= 4x₁ - 1x₂ a. Write the above system in matrix form ie = Ax. What is A? dx dt b. Find et (Use the full process I showed in class, using the associated linear differential equation and finding its natural fundamental set of solutions associated to time t = 0. Then, do it again with the Two-by-Two Matrix Exponential Formulas in section 4.3 of book.) Give a general solution of the system. d. Give the solution of the IVP with initial value x(0) = (3) e. Give the solution of the IVP with initial value x(1) = 3 using e¹A
Transcribed Image Text:2. Given the system dx₁ dt dx dt C. = 3x₂ + 3x₂ -= 4x₁ - 1x₂ a. Write the above system in matrix form ie = Ax. What is A? dx dt b. Find et (Use the full process I showed in class, using the associated linear differential equation and finding its natural fundamental set of solutions associated to time t = 0. Then, do it again with the Two-by-Two Matrix Exponential Formulas in section 4.3 of book.) Give a general solution of the system. d. Give the solution of the IVP with initial value x(0) = (3) e. Give the solution of the IVP with initial value x(1) = 3 using e¹A
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