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• 20:32, 10 October 2026 Rongzhou talk contribs created page Linear differential equation (Created page with "A linear differential equation of order $n$ has the general form {{#content:Q2136}} When $f(\mathbf{x})=0$, the differential equation is further said to be '''homogeneous'''. == Properties == === Superposition === Consider the linear differential equation $$ \sum_{|\alpha|\le m} a_\alpha(\mathbf{x})\,D^\alpha u(\mathbf{x})=f(\mathbf{x}), $$ as a linear operator $L[u]$, by definition of linearity $$ L[c_1u_1+c_2u_2\cdots +c_nu_n]=c_1L[u_1]+c_2L[u_2]+\cdots c_nL[u...")