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The problem of deducing the basic relative invariants possessed by monic homogeneous linear differential equations of order $m$ was initiated in 1879 with Edmund Laguerres success for the special case $m = 3$. It was solved in number 744 of theMoreThe problem of deducing the basic relative invariants possessed by monic homogeneous linear differential equations of order $m$ was initiated in 1879 with Edmund Laguerres success for the special case $m = 3$. It was solved in number 744 of the Memoirs of the AMS (March 2002), by a procedure that explicitly constructs, for any $m /geq3$, each of the $m - 2$ basic relative invariants. During that 123-year time span, only a few results were published about the basic relative invariants for other classes of ordinary differential equations. With respect to any fixed integer $/,m /geq 1$, the author begins by explicitly specifying the basic relative invariants for the class $/,/mathcal{C {m,2 $ that contains equations like $Q {m = 0$ in which $Q {m $ is a quadratic form in $y(z), /, /dots, /, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $/bigl( y{(m) (z) /bigr){2 $ is $1$.Then, in terms of any fixed positive integers $m$ and $n$, the author explicitly specifies the basic relative invariants for the class $/,/mathcal{C {m,n $ that contains equations like $H {m,n = 0$ in which $H {m,n $ is an $n$th-degree form in $y(z), /, /dots, /, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $/bigl( y{(m) (z) /bigr){n $ is $1$. These results enable the author to obtain the basic relative invariants for additional classes of ordinary differential equations. Basic Global Relative Invariants for Nonlinear Differential Equations by Roger Chalkley