常微分方程求解,要步骤,谢谢
发布网友
发布时间：2024-10-24 07:59
共1个回答
热心网友
时间：2024-10-25 07:50
dx/x = - λdt, lnx = - λt + lnC, x = Ce^(-λt),
x(0) = 1100, C = 1100, x = 1100e^(-λt).
dy/dt + μy = 1100λe^(-λt)
y = e^(∫-μdt) [∫1100λe^(-λt)e^(∫μdt)dt + D]
= e^(-μt) [1100λ∫e^(-λt)e^(μt)dt + D]
= e^(-μt) [1100λ∫e^(μ-λ)tdt + D]
= e^(-μt) [1100λe^(μ-λ)t/(μ-λ) + D]
= 100λe^(-λ)t/(μ-λ) + De^(-μt),
y(0) = 0, D = -100λ/(μ-λ) ,
y = [100λ/(μ-λ)] [e^(-λ)t - e^(-μt)].
