{"entities":{"Q1662":{"pageid":3308,"ns":120,"title":"Item:Q1662","lastrevid":7341,"modified":"2026-09-04T07:28:01Z","type":"item","id":"Q1662","labels":{"en":{"language":"en","value":"Substituting the exponential trial solution into the homogeneous equation"}},"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":"Q1662$94E4AE28-F116-47F2-BB5D-42CBDCA0DD5A","rank":"normal"}],"P4":[{"mainsnak":{"snaktype":"value","property":"P4","hash":"d75f0c19ffdd8f220b57f61d4b93fedb6cf9f558","datavalue":{"value":"y=e^{rx},\\\\quad y'=r\\\\,e^{rx},\\\\quad y''=r^{2}\\\\,e^{rx};\\\\qquad y''+a\\\\,y'+b\\\\,y=\\\\bigl(r^{2}+a\\\\,r+b\\\\bigr)e^{rx}=0\\\\ \\\\Rightarrow\\\\ r^{2}+a\\\\,r+b=0,\\\\quad e^{rx}\\\\neq 0","type":"string"},"datatype":"string"},"type":"statement","id":"Q1662$6B4BD6FC-9943-4706-A87F-254526A315AD","rank":"normal"}]},"sitelinks":{}}}}