{"entities":{"Q1666":{"pageid":3312,"ns":120,"title":"Item:Q1666","lastrevid":7349,"modified":"2026-09-04T07:28:02Z","type":"item","id":"Q1666","labels":{"en":{"language":"en","value":"Solving the variation-of-parameters system with Cramer's rule and the Wronskian"}},"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":"Q1666$85B34E33-C01E-4075-834E-BD494997956C","rank":"normal"}],"P4":[{"mainsnak":{"snaktype":"value","property":"P4","hash":"5fea2ecd0c49406086eeab8c6ce9848fd67f670e","datavalue":{"value":"\\\\begin{pmatrix}y_{1}&y_{2}\\\\\\\\ y_{1}'&y_{2}'\\\\end{pmatrix}\\\\binom{u_{1}'}{u_{2}'}=\\\\binom{0}{g},\\\\qquad W=y_{1}y_{2}'-y_{2}y_{1}';\\\\qquad u_{1}'=\\\\frac{\\\\begin{vmatrix}0&y_{2}\\\\\\\\ g&y_{2}'\\\\end{vmatrix}}{W}=-\\\\frac{y_{2}\\\\,g}{W},\\\\qquad u_{2}'=\\\\frac{\\\\begin{vmatrix}y_{1}&0\\\\\\\\ y_{1}'&g\\\\end{vmatrix}}{W}=\\\\frac{y_{1}\\\\,g}{W}","type":"string"},"datatype":"string"},"type":"statement","id":"Q1666$DB300270-0608-4327-BED1-324FD703037B","rank":"normal"}]},"sitelinks":{}}}}