{"entities":{"Q1613":{"pageid":3229,"ns":120,"title":"Item:Q1613","lastrevid":7266,"modified":"2026-09-03T19:22:01Z","type":"item","id":"Q1613","labels":{"en":{"language":"en","value":"Integrating factor for a linear first-order 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":"Q1613$DAF7C61B-CC48-44F7-A169-99B39C47B472","rank":"normal"}],"P4":[{"mainsnak":{"snaktype":"value","property":"P4","hash":"f26001da4aa83f480c5b8e27bbd0461b9e35da50","datavalue":{"value":"\\\\frac{dy}{dx}+p(x)\\\\,y=q(x),\\\\text{multiply both sides by } \\\\mu(x)=e^{\\\\int p(x)\\\\,dx}\\\\;\\\\Longrightarrow\\\\;\\\\frac{d}{dx}\\\\bigl(\\\\mu(x)\\\\,y\\\\bigr)=\\\\mu(x)\\\\,q(x)","type":"string"},"datatype":"string"},"type":"statement","id":"Q1613$7F4B7B3D-726E-4BD9-842D-698E2C2BF2A0","rank":"normal"}]},"sitelinks":{}}}}