Question

In each of Problems 7 through 10: (a) Find the solution of the given initial value problem. (b) Draw the trajectory of the solution in the $x_1x_2$-plane, and also draw the graph of $x_1$ versus $t$. 7. $x' = egin{pmatrix} 1 & -4 \ 4 & -7 end{pmatrix} x$, $x(0) = egin{pmatrix} 3 \ 2 end{pmatrix}$ 8. $x' = egin{pmatrix} -frac{5}{2} & frac{3}{2} \ -frac{3}{2} & frac{1}{2} end{pmatrix} x$, $x(0) = egin{pmatrix} 3 \ -1 end{pmatrix}$ 9. $x' = egin{pmatrix} 2 & frac{3}{2} \ -frac{3}{2} & -1 end{pmatrix} x$, $x(0) = egin{pmatrix} 3 \ -2 end{pmatrix}$ 10. $x' = egin{pmatrix} 3 & 9 \ -1 & -3 end{pmatrix} x$, $x(0) = egin{pmatrix} 2 \ 4 end{pmatrix}$

          In each of Problems 7 through 10:
(a) Find the solution of the given initial value problem.
(b) Draw the trajectory of the solution in the $x_1x_2$-plane, and also draw the graph of $x_1$ versus $t$.
7. $x' = egin{pmatrix} 1 & -4 \ 4 & -7 end{pmatrix} x$, $x(0) = egin{pmatrix} 3 \ 2 end{pmatrix}$
8. $x' = egin{pmatrix} -frac{5}{2} & frac{3}{2} \ -frac{3}{2} & frac{1}{2} end{pmatrix} x$, $x(0) = egin{pmatrix} 3 \ -1 end{pmatrix}$
9. $x' = egin{pmatrix} 2 & frac{3}{2} \ -frac{3}{2} & -1 end{pmatrix} x$, $x(0) = egin{pmatrix} 3 \ -2 end{pmatrix}$
10. $x' = egin{pmatrix} 3 & 9 \ -1 & -3 end{pmatrix} x$, $x(0) = egin{pmatrix} 2 \ 4 end{pmatrix}$

$In each of Problems 7 through 10: (a) Find the solution of the given initial value problem. (b) Draw the trajectory of the solution in the x1x2-plane, and also draw the graph of x1 versus t. 7. x' = eginpmatrix 1 -4 4 -7 endpmatrix x, x(0) = eginpmatrix 3 2 endpmatrix 8. x' = eginpmatrix -frac52 frac32 -frac32 frac12 endpmatrix x, x(0) = eginpmatrix 3 -1 endpmatrix 9. x' = eginpmatrix 2 frac32 -frac32 -1 endpmatrix x, x(0) = eginpmatrix 3 -2 endpmatrix 10. x' = eginpmatrix 3 9 -1 -3 endpmatrix x, x(0) = eginpmatrix 2 4 endpmatrix$

Added by Ronald L.

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