1. Consider the following second order linear equation with initial conditions (IVP): e'y" + y – y = 0, y(0) = 1, y'(0) = -1 (a) Convert the above initial value problem to an equivalent first-order linear system by defining new dependent variables x1(t), x2(t). Don't forget the initial values. (b) Write the IVP in part (a) using matrix-vector notation as ' = AT, 7(0) = xồ, where 7 (t) = :

1. Consider the following second order linear equation with initial conditions (IVP): e'y" + y – y = 0, y(0) = 1, y'(0) = -1 (a) Convert the above initial value problem to an equivalent first-order linear system by defining new dependent variables x1(t), x2(t). Don't forget the initial values. (b) Write the IVP in part (a) using matrix-vector notation as ' = AT, 7(0) = xồ, where 7 (t) = :

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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