方程一
已知(C, D)都是长度为(n)的多项式,求(F), (F′=Ce^F+D pmod {x^n})
Sol:
[egin{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}
]
[egin{aligned}
设U' = TU, frac{dU}{dx} &= TU \
ln(U) &= int T dx \
U &= e^{int Tdx}
end{aligned}
]
[egin{aligned}
设F = UV, (UV)' &= TUV + Z \
UV' + VU' &= U'V + Z\
V &= int frac {Z}{U}
end{aligned}
]
方程二
[egin {aligned}
F &= int e^{T-F}dx \
e^F F' &= e^T \
e^F &= int e^T + 1 \
F &= lnleft (int e^T + 1
ight)
end {aligned}
]
留坑链式反应