01A41
幼苗
共回答了22个问题采纳率:95.5% 举报
齐次方程2000dC/dt + 7.2C = 0
dC/C = -7.2/2000 *dt
∫dC/C = ∫-7.2/2000 * dt
ln C = -7.2/2000 * t
通解C = Ae^(-7.2/2000 * t) ,A为常数
设 C = A(t) * e^(-7.2/2000 * t) ,因为 C(0) = 0,所以 A(0) = 0
代入原方程
2000 A'(t) * e^(-7.2/2000 * t) + 2000A(t) * e^(-7.2/2000 * t) * (-7.2/2000) = x/60 - 7.2 A(t) * e^(-7.2/2000 * t)
2000A'(t) * e^(-7.2/2000 * t) = x/60
A'(t) = x/120000 * e ^ (7.2/2000 * t)
A(t) = ∫x/120000 * e ^ (7.2/2000 * t) dt = x/ 120000 * e^(7.2/2000 * t) * 2000/7.2
A(t) = x/(60*7.2) * e^(7.2/2000 * t) = x/432 * e^(7.2/2000 * t)
A(0) = x/432 = 0
x = 0
上面直接敲的,可能有误,但解法就是按常系数的一阶微分方程的解法去解
1年前
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