Solving the variation-of-parameters system with Cramer's rule and the Wronskian (Q1666): Difference between revisions

\\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}