Linear differential operator
= Linear differential operator
{title2=$L=\sum_{j=0}^m a_j(x)D^j$}
A linear <differential operator> is a finite linear combination of <derivatives> with specified coefficient <functions>. It obeys $L(\alpha f+\beta g)=\alpha Lf+\beta Lg$ for scalar constants $\alpha,\beta$. Variable coefficients need not commute with <differentiation>: $D(af)=a'f+af'$.