解方程
作者：互联网
题意
已知\(C, D\)都是长度为\(n\)的多项式,求\(F\), \(F′=Ce^F+D \pmod {x^n}\)
Sol:
\[ \begin{aligned} F' = G(F) &= Ce^F + D \\ &= G(F_0) + G'(F_0) (F - F_0) \\ &= Ce^{F_0} + D + Ce^{F_0}(F - F_0) \\ &= TF + Z \end{aligned} \]
\[ \begin{aligned} 设U' = TU, \frac{dU}{dx} &= TU \\ \ln(U) &= \int T dx \\ U &= e^{\int Tdx} \end{aligned} \]
\[ \begin{aligned} 设F = UV, (UV)' &= TUV + Z \\ UV' + VU' &= U'V + Z\\ V &= \int \frac {Z}{U} \end{aligned} \]
标签：begin,end,int,UV,Ce,解方程,aligned 来源： https://www.cnblogs.com/foreverpiano/p/10547596.html