Given a system of first order linear differential equations

{x' = f(x,y), y' = g(x,y)}

Solve one of the equations for x (or y) to get an equation of the form

{x = c_1y' + c_2y}

Differentiate to get

{x' = c_1y'' + c_2y'}.

and substitue these expressions into the other equation and solve using second order methods.

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