(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Convert y"=0 to a first-order system du/dt=Au

d/dt [y y']^{T}= [y' 0]^{T}= [0 1; 0 0] [y y']^{T}

This 2x2 matrix A has only one eigenvector and cannot be diagonalized. Compute e^{At}from the series I+At+... and write the solution e^{At}u(0) starting from y(0)=3, y'(0)=4. Check that your (y, y') satisfies y"=0.

2. Relevant equations

3. The attempt at a solution

So I found e^{At}to be equal to the matrix

[1 t

0 1].

I found this e^{At}=I+At where A is the matrix [0 1; 0 0].

I also know that matrix A has eigenvalue 0 with multiplicity 2, and eigenvector [1 0]^{T}.

But from there I'm stuck... Not sure how to get e^{At}u(0)...

Can anyone help? Thanks in advance!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Second-Order Equations and Eigenvectors

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