{"type":"rich","version":"1.0","title":"Solving the variation-of-parameters system with Cramer's rule and the Wronskian","html":"<span class=\"wb-embed wb-embed-math\" data-latex=\"\\begin{pmatrix}y_{1}&amp;y_{2}\\\\ y_{1}'&amp;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&amp;y_{2}\\\\ g&amp;y_{2}'\\end{vmatrix}}{W}=-\\frac{y_{2}\\,g}{W},\\qquad u_{2}'=\\frac{\\begin{vmatrix}y_{1}&amp;0\\\\ y_{1}'&amp;g\\end{vmatrix}}{W}=\\frac{y_{1}\\,g}{W}\">\\begin{pmatrix}y_{1}&amp;y_{2}\\\\ y_{1}'&amp;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&amp;y_{2}\\\\ g&amp;y_{2}'\\end{vmatrix}}{W}=-\\frac{y_{2}\\,g}{W},\\qquad u_{2}'=\\frac{\\begin{vmatrix}y_{1}&amp;0\\\\ y_{1}'&amp;g\\end{vmatrix}}{W}=\\frac{y_{1}\\,g}{W}</span>","width":640,"height":320}