Can some one help me out with the L operator of a linear differential equation?

06 June 2014 1 4K Report

Lu=d2u(x)/dx2. What is the meaning of this expression? The R.H.S is a second order derivative.

L is a linear operation on u, means that it can be any operation or combination of operations that follow linearity [that is the combination of which under addition is also linear, e.g. if one operation L(u)=a*u+b, then L(c1*u+c2*u) is "linear" L(u) in the sense that it equals c1*L(u)+c2*L(u). Also L(u) could contain a du/dx term for instance, but it doesn't work if you have square root term or quadratic, because sqrt(a+b) is not related to sqrt(a)+sqrt(b)

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