Sketching Phase Curve Diagrams

Suppose we have the system of coupled differential equations


Phase space diagrams illustrate the direction of the velocity field, in this example  
\[\begin{pmatrix}\dot{x}\\ \dot{y}\end{pmatrix}=\begin{pmatrix}x+2y\\y\end{pmatrix}\]
At each point  
  draw the vector  

We can sketch curves - phase curves - to illustrate the velocity profile of the system by drawing smooth curves in the direction of the arrows at each point.

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