姓名 ______________________日期 ____________得分 ____ / 12
微积分练习
微分方程：初值问题 · 1–6
在给定的初始条件下解微分方程。
1.dydx = 3x2 − 2x − 6, y(0) = −8
2.dydx = −6x2 − 8x + 1, y(0) = 3
3.dydx = 3x2 + 8x + 2, y(0) = −3
4.dydx = −3x2 + 6x − 6, y(0) = −5
5.dydx = −3x2 − 8x − 9, y(0) = −3
6.dydx = 6x2 − 4x − 2, y(0) = 7
指数增长与衰减模型（dy/dt = ky） · 7–12
用 y = y₀e^(kt)，结果精确到百分位。
7.dydt = −0.05y, y(0) = 280y(2) ≈
8.dydt = −0.05y, y(0) = 310y(5) ≈
9.dydt = −0.12y, y(0) = 270y(10) ≈
10.dydt = −0.11y, y(0) = 20y(4) ≈
11.dydt = −0.11y, y(0) = 50y(5) ≈
12.dydt = −0.15y, y(0) = 460y(5) ≈
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