Decoupling ODEs

-The solutions are well known functions.
-There exist EODE class that does not cover linear systems in one semester?
If decoupling the odes is what you whant to do just solve for each variable (trivial) and substitute one into the other.
solve
[tex]x=\frac{dy}{dt}[/tex]
[tex]y=-\frac{dx}{dt}[/tex]
substitute
[tex]x=\frac{dy}{dt}=\frac{d}{dt}\left(-\frac{dx}{dt}\right)=-\frac{d^2x}{dt^2}[/tex]
[tex]y=-\frac{dx}{dt}=-\frac{d}{dt}\left(\frac{dy}{dt}\right)=-\frac{d^2y}{dt^2}[/tex]
Decoupled
Now as for finding soulutions I heard somewhere that some special functions having something to do with cirlces and triangles has something to do with it.
Also be aware you have introduced extraneous solutions so eliminate them be substituting into the original equation.