General linear differential equation of order n (Q2136)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | General linear differential equation of order n |
No description defined |
Statements
\\sum_{|\\alpha|\\le m} a_\\alpha(\\mathbf{x})\\,D^\\alpha u(\\mathbf{x})=f(\\mathbf{x}),\n\\qquad \n\\mathbf{x}=(x_1,\\dots,x_d).
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Where:\n\n$a_\\alpha(\\mathbf{x})$ and $f(\\mathbf{x})$ are functions of $\\mathbf{x}$,\n\n$$\n\\alpha=(\\alpha_1,\\dots,\\alpha_d),\n\\qquad \n|\\alpha|=\\alpha_1+\\cdots+\\alpha_d,\n$$\n\nand \n\n$$\nD^\\alpha u=\n\\frac{\\partial^{|\\alpha|}u}\n{\\partial x_1^{\\alpha_1}\\cdots \\partial x_d^{\\alpha_d}}.\n$$
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