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## Homework Statement

dx/dt = -xy

dy/dt =-xy

find x(t) and y(t)

## The Attempt at a Solution

Using Maple I've plotted the vector field and solution curve for a list of initial conditions. When I tried to work by hand I could find a way to uncoulple the equations. Is there an analytical solution? Method (linearization and etc. )works best? I've sifted through numerous textbooks and couldn't find a decent example.