Classify the origin of the following linear systems as source, sink, spiral source, spiral
sink, centre, sink with repeated eigenvalues, etc. In each case compute the eigenvalues of
the coefficient matrix and use this to determine the type, without solving the system. In
each complex case determine whether the solution spirals clockwise or counterclockwise.

dx/dt= 2x − y
dy/dt= 3x + 4y

Question

Classify the origin of the following linear systems as source, sink, spiral source, spiral
sink, centre, sink with repeated eigenvalues, etc. In each case compute the eigenvalues of
the coefficient matrix and use this to determine the type, without solving the system. In
each complex case determine whether the solution spirals clockwise or counterclockwise.

dx/dt= 2x − y
dy/dt= 3x + 4y