{"entities":{"Q2136":{"pageid":4198,"ns":120,"title":"Item:Q2136","lastrevid":9718,"modified":"2026-10-10T20:28:48Z","type":"item","id":"Q2136","labels":{"en":{"language":"en","value":"General linear differential equation of order n"}},"descriptions":{},"aliases":{},"claims":{"P1":[{"mainsnak":{"snaktype":"value","property":"P1","hash":"6056844c4a6d3699fbafab69805eed5ca36eab0e","datavalue":{"value":{"entity-type":"item","numeric-id":4,"id":"Q4"},"type":"wikibase-entityid"},"datatype":"wikibase-item"},"type":"statement","id":"Q2136$773EC0CB-AB4F-4D23-B930-8C604D8E1F8B","rank":"normal"}],"P4":[{"mainsnak":{"snaktype":"value","property":"P4","hash":"ddbf6135b131f2ba859e47f2316a46f3b4a00c5d","datavalue":{"value":"\\\\sum_{|\\\\alpha|\\\\le m} a_\\\\alpha(\\\\mathbf{x})\\\\,D^\\\\alpha u(\\\\mathbf{x})=f(\\\\mathbf{x}),\\n\\\\qquad \\n\\\\mathbf{x}=(x_1,\\\\dots,x_d).","type":"string"},"datatype":"string"},"type":"statement","id":"Q2136$F7E4323E-EC6C-4AEB-ACB2-9A297170B2A8","rank":"normal"}],"P75":[{"mainsnak":{"snaktype":"value","property":"P75","hash":"55c8f69d615df446e25aa2c40fea9fa95b019976","datavalue":{"value":"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$$\\nD^\\\\alpha u=\\n\\\\frac{\\\\partial^{|\\\\alpha|}u}\\n{\\\\partial x_1^{\\\\alpha_1}\\\\cdots \\\\partial x_d^{\\\\alpha_d}}.\\n$$","type":"string"},"datatype":"string"},"type":"statement","id":"Q2136$CF2B0A17-F88B-4FB9-811F-6507F29FBF39","rank":"normal"}],"P6":[{"mainsnak":{"snaktype":"value","property":"P6","hash":"d92372df44774f866200aa6fd16439ffabdc85d9","datavalue":{"value":{"entity-type":"item","numeric-id":147,"id":"Q147"},"type":"wikibase-entityid"},"datatype":"wikibase-item"},"type":"statement","id":"Q2136$5CA4FF49-32FD-45F5-B71D-3FEB20A14BE1","rank":"normal"}]},"sitelinks":{}}}}