WeBWorK Standalone Renderer

Match each initial value problem with the phase plane plot of its solution. (The arrows on the curves indicate how the solution point moves as $t$ increases.)

1. $\displaystyle \boldsymbol{\vec{y}^{\,\prime}} = \left\lbrack \begin{array}{rr} 1 & -0.5 \\ 0.5 & 1 \end{array} \right\rbrack \boldsymbol{\vec{y}}, \ \ \ \boldsymbol{\vec{y}}(0) = \left\lbrack \begin{array}{r} 1 \\ 0 \end{array} \right\rbrack.$

2. $\displaystyle \boldsymbol{\vec{y}^{\,\prime}} = \left\lbrack \begin{array}{rr} 0 & -1 \\ 1 & 0 \end{array} \right\rbrack \boldsymbol{\vec{y}}, \ \ \ \boldsymbol{\vec{y}}(0) = \left\lbrack \begin{array}{r} 1 \\ 0 \end{array} \right\rbrack.$

3. $\displaystyle \boldsymbol{\vec{y}^{\,\prime}} = \left\lbrack \begin{array}{rr} 0 & 2 \\ -2 & 0 \end{array} \right\rbrack \boldsymbol{\vec{y}}, \ \ \ \boldsymbol{\vec{y}}(0) = \left\lbrack \begin{array}{r} 1 \\ 0 \end{array} \right\rbrack.$

4. $\displaystyle \boldsymbol{\vec{y}^{\,\prime}} = \left\lbrack \begin{array}{rr} -1 & -0.5 \\ 0.5 & -1 \end{array} \right\rbrack \boldsymbol{\vec{y}}, \ \ \ \boldsymbol{\vec{y}}(0) = \left\lbrack \begin{array}{r} 1 \\ 0 \end{array} \right\rbrack.$



A		B



C		D

In order to get credit for this problem all answers must be correct.