{"entities":{"Q1645":{"pageid":3283,"ns":120,"title":"Item:Q1645","lastrevid":7289,"modified":"2026-09-03T19:39:50Z","type":"item","id":"Q1645","labels":{"en":{"language":"en","value":"Real general solution for complex-conjugate characteristic roots"}},"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":"Q1645$58AFADCE-0611-44F1-A01C-07741FDB58BA","rank":"normal"}],"P4":[{"mainsnak":{"snaktype":"value","property":"P4","hash":"8c3b970dab1064abd64552ee194218d60eb1c8cd","datavalue":{"value":"r=\\\\alpha\\\\pm i\\\\beta\\\\ \\\\Rightarrow\\\\ y=e^{\\\\alpha x}\\\\bigl(C_{1}\\\\cos\\\\beta x+C_{2}\\\\sin\\\\beta x\\\\bigr)","type":"string"},"datatype":"string"},"type":"statement","id":"Q1645$6E60CBC8-C827-4FA8-81BD-37B027C53502","rank":"normal"}]},"sitelinks":{}}}}