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## Homework Statement

Show that the vectors

[tex]\overline{x}(t) =

\begin{bmatrix}

e^t

\\ -t

\end{bmatrix}

[/tex]

and

[tex]

\overline{y}(t) =

\begin{bmatrix}

t

\\ e^(-t)

\end{bmatrix}[/tex]

are solutions for

[tex]\overline{x}' = \frac {1} {1+t^2}

\begin{bmatrix}

1+t & e^t(1-t)

\\ -e^-(t) (1+t) & t-1

\end{bmatrix}

\overline{x}

.[/tex]

The last row should be a 2x2 matrix. The x and y are vectors.

## The Attempt at a Solution

I feel that it would be helpful to have fundamental matrix here: [itex]\Phi(t,s)[/itex].