{"type":"rich","version":"1.0","title":"Variation of parameters: the first determining condition and its effect on yp'","html":"<span class=\"wb-embed wb-embed-math\" data-latex=\"y_{p}=u_{1}y_{1}+u_{2}y_{2}\\quad\\Rightarrow\\quad y_{p}'=u_{1}'y_{1}+u_{2}'y_{2}+u_{1}y_{1}'+u_{2}y_{2}';\\qquad u_{1}'y_{1}+u_{2}'y_{2}=0\\ \\Rightarrow\\ y_{p}'=u_{1}y_{1}'+u_{2}y_{2}'\">y_{p}=u_{1}y_{1}+u_{2}y_{2}\\quad\\Rightarrow\\quad y_{p}'=u_{1}'y_{1}+u_{2}'y_{2}+u_{1}y_{1}'+u_{2}y_{2}';\\qquad u_{1}'y_{1}+u_{2}'y_{2}=0\\ \\Rightarrow\\ y_{p}'=u_{1}y_{1}'+u_{2}y_{2}'</span>","width":640,"height":320}