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Magazine Problem 1
Determine the location and type of all critical points by linearization. $$\begin{array}{l}y_{1}^{\prime}=y_{2}+y_{2}^{2} \\\y_{2}^{\prime}=3 y_{1}\end{array}$$
Problem 1
Determine the type and stability of the critical point Then find a real general solution and sketch or graph some of the trajoctories in the phase plane. (Show the details of your work.) $$\begin{aligned}&y_{1}^{\prime}=2 y_{2}\\\&y_{2}^{\prime}=8 y_{2}\end{aligned}$$
Problem 1
Find a real general solution of the following systems. (Show the details.) $$\begin{aligned} &y_{1}^{\prime}=3 y_{2}\\\ &y_{2}^{\prime}=12 y_{1} \end{aligned}$$
Problem 2
Determine the location and type of all critical points by linearization. $$\begin{array}{l}y_{1}^{\prime}=4 y_{1}-y_{1}^{2} \\\y_{2}^{\prime}=y_{2}\end{array}$$
Problem 2
Find a general solution. (Show the details of your work.) $$\begin{aligned}&y_{1}^{\prime}=y_{2}+t\\\&y_{2}^{\prime}-y_{1}-3 t\end{aligned}$$
Problem 2
Find a real general solution of the following systems. (Show the details.) $$\begin{aligned} &y_{1}^{\prime}=5 y_{2}\\\ &y_{2}^{\prime}=5 y_{1} \end{aligned}$$
Problem 3
Find a real general solution of the following systems. (Show the details.) $$\begin{array}{l} y_{1}^{\prime}=y_{1}+y_{2} \\ y_{2}^{\prime}=y_{1}+y_{2} \end{array}$$
Problem 3
Find a general solution. (Show the details of your work.) $$\begin{array}{l}y_{1}^{\prime}=4 y_{2}+9 t \\\y_{2}^{\prime}=-4 y_{1}+5\end{array}$$
Problem 3
Determine the location and type of all critical points by linearization. $$\begin{aligned}&y_{1}^{\prime}=4 y_{2}\\\&y_{2}^{\prime}=2 y_{1}-y_{2}^{2}\end{aligned}$$
Problem 4
Determine the location and type of all critical points by linearization. $$\begin{aligned}&y_{1}^{\prime}=-3 y_{1}+y_{2}-y_{2}^{2}\\\&y_{2}^{\prime}=y_{1}-3 y_{2}\end{aligned}$$
