對于Robin Gan最新一期視頻中題目的解析

2022-10-12 01:54 作者:げいしも_蕓 0人讀過 | 我要投稿

$%E6%B1%82%E8%A7%A3%E4%B8%80%E9%98%B6%E9%9D%9E%E9%BD%90%E6%AC%A1%E7%BA%BF%E6%80%A7%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%EF%BC%9A$

$%5Cfrac%7B%5Ctext%20dy%7D%7B%5Ctext%20dt%7D%2B%5Cfrac%7B2t%2B3%7D%7Bt%5E2%2B3t%2B6%7Dy%3D%5Cfrac%7B1%7D%7Bt(t%5E2-2t%2B2)%7D%2Cy%5Cvert_%7Bt%3D1%7D%3D0$

解：

$%E5%AF%B9%E5%BA%94%E9%BD%90%E6%AC%A1%E6%96%B9%E7%A8%8B%E4%B8%BA%EF%BC%9A%5Cfrac%7B%5Ctext%20dY%7D%7B%5Ctext%20dt%7D%2B%5Cfrac%7B2t%2B3%7D%7Bt%5E2%2B3t%2B6%7DY%3D0$

$%E5%88%86%E7%A6%BB%E5%8F%82%E6%95%B0%E5%BE%97%EF%BC%9A%5Cfrac%7B%5Ctext%20dY%7DY%3D%5Cfrac%7B%5Ctext%20d(t%5E2%2B3t%2B6)%7D%7Bt%5E2%2B3t%2B6%7D$

$%E4%B8%A4%E7%AB%AF%E7%A7%AF%E5%88%86%EF%BC%9A%5Cln%5Cvert%20Y%5Cvert%3D-%5Cln(t%5E2%2B3t%2B6)%2BC_1$

$%E5%BE%97%E5%88%B0%EF%BC%9AY%3D%5Cfrac%7BC_2%7D%7Bt%5E2%2B3t%2B6%7D(C_2%3D%5Cpm%20e%5E%7BC_1%7D)$

$%E5%88%A9%E7%94%A8%E5%B8%B8%E6%95%B0%E5%8F%98%E6%98%93%E6%B3%95%EF%BC%8C%E4%BB%A4%EF%BC%9Ay%3D%5Cfrac%7Bu%7D%7Bt%5E2%2B3t%2B6%7D%EF%BC%8C%E5%85%B6%E4%B8%ADu%3Du(t)$

$%E6%9C%89%EF%BC%9A%5Cfrac%7B%5Ctext%20dy%7D%7B%5Ctext%20dt%7D%3D%5Cfrac%7Bu'(t%5E2%2B3t%2B6)-u(2t%2B3)%7D%7B(t%5E2%2B3t%2B6)%5E2%7D%3D%5Cfrac%7Bu'%7D%7Bt%5E2%2B3t%2B6%7D-%5Cfrac%7Bu(2t%2B3)%7D%7Bt%5E2%2B3t%2B6%7D$

$%E4%BB%A3%E5%85%A5%E5%8E%9F%E5%BC%8F%E5%BE%97%EF%BC%9A%5Cfrac%7Bu'%7D%7Bt%5E2%2B3t%2B6%7D-%5Cfrac%7Bu(2t%2B3)%7D%7Bt%5E2%2B3t%2B6%7D%2B%5Cfrac%7B2t%2B3%7D%7Bt%5E2%2B3t%2B6%7D%5Cleft(%5Cfrac%7Bu%7D%7Bt%5E2%2B3t%2B6%7D%5Cright)%3D%5Cfrac1%7Bt(t%5E2-2t%2B2)%7D$

$%E5%8D%B3%EF%BC%9A%5Cfrac%7Bu'%7D%7Bt%5E2%2B3t%2B6%7D%3D%5Cfrac%7B1%7D%7Bt(t%5E2-2t%2B2)%7D%2Cu%3D%5Cint%5Cfrac%7Bt%5E2%2B3t%2B6%7D%7Bt(t%5E2-2t%2B2)%7D%5Ctext%20dt$

$%E8%AE%BE%5Cint%5Cfrac%7Bt%5E2%2B3t%2B6%7D%7Bt(t%5E2-2t%2B2)%7D%5Ctext%20dt%3D%5Cint%5Cleft%20(%5Cfrac%7BA_1%7D%7Bt%7D%2B%5Cfrac%7BB_2t%2BA_2%7D%7Bt%5E2-2t%2B2%7D%5Cright)%5Ctext%20dt$

$%E5%8F%AF%E4%BB%A5%E5%BE%97%E5%88%B0%EF%BC%9A%0A%5Cleft%20%5C%7B%0A%5Cbegin%7Baligned%7D%0AA_1%2BB_2%3D1%5C%5C%0A-2A_1%2BA_2%3D3%5C%5C%0A2A_1%3D6%0A%5Cend%7Baligned%7D%0A%5Cright.%0A%EF%BC%8C%E8%A7%A3%E5%BE%97%EF%BC%9A%0A%5Cleft%20%5C%7B%0A%5Cbegin%7Baligned%7D%0AA_1%3D3%5C%5C%0AA_2%3D9%5C%5C%0AB_2%3D-2%0A%5Cend%7Baligned%7D%0A%5Cright.$

$%E4%BA%8E%E6%98%AFu%3D%5Cint%5Cleft%20(%5Cfrac%7BA_1%7D%7Bt%7D%2B%5Cfrac%7BB_2t%2BA_2%7D%7Bt%5E2-2t%2B2%7D%5Cright)%5Ctext%20dt%3D%0A%5Cint%5Cleft%20(%5Cfrac%7B3%7D%7Bt%7D%2B%5Cfrac%7B-2t%2B9%7D%7Bt%5E2-2t%2B2%7D%5Cright)%5Ctext%20dt$

$%3D3%5Cint%5Cfrac%7B1%7D%7Bt%7D%5Ctext%20dt-2%5Cint%5Cfrac%7Bt%7D%7Bt%5E2-2t%2B2%7D%2B9%5Cint%5Cfrac%7B1%7D%7Bt%5E2-2t%2B2%7D%5Ctext%20dt$

$%3D3%5Cln%5Cvert%20t%5Cvert-2%5Cint%5Cfrac%7Bt%7D%7Bt%5E2-2t%2B2%7D%2B9%5Cint%5Cfrac%7B%5Ctext%20d(t-1)%7D%7B(t-1)%5E2%2B1%7D$

$%3D3%5Cln%5Cvert%20t%5Cvert-2%5Cint%5Cfrac%2012%5Cleft%20(%5Cfrac%7B2t-2%7D%7Bt%5E2-2t%2B2%7D%2B%5Cfrac%7B2%7D%7Bt%5E2-2t%2B2%7D%5Cright)%5Ctext%20dt%2B9%5Cint%5Cfrac%7B%5Ctext%20d(t-1)%7D%7B(t-1)%5E2%2B1%7D$

$%3D3%5Cln%5Cvert%20t%20%5Cvert%20-%5Cint%5Cfrac%7B%5Ctext%20d(t%5E2-2t%2B2)%7D%7Bt%5E2-2t%2B2%7D%2B7%5Cint%5Cfrac%7B%5Ctext%20d(t-1)%7D%7B(t-1)%5E2%2B1%7D$