Linear differential equation: Revision history

10 October 2026

• curprev 20:3320:33, 10 October 2026 Rongzhou talk contribs 1,312 bytes +4 No edit summary
• curprev 20:3220:32, 10 October 2026 Rongzhou talk contribs 1,308 bytes +1,308 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..."