Find an explicit particular solution of the differential equation:
dx / dt = (2 - e^t) / (3 + 2x)
subject to the condition x(0) = 0.
At what value of t does your solution attain a stationary value?
3 days ago
Additional Details
Is there another way to do this that split and integrate to get all in terms of x instead of the exponential ?
maths differential eq
2010-02-14 12:56 pm
回答 (1)
2010-02-14 4:47 pm
✔ 最佳答案
dx/dt = (2 - e^t) / (3 + 2x)Using separating variables,
ʃ(3 + 2x) dx = ʃ(2 - e^t) dt
3x + x^2 = 2t - e^t + Cx(0) = 0So, 0 = 0 - e^0 + CC = 1So, 3x + x^2 = 2t - e^t + 1To attain a stationary value, dx/dt = 02 - e^t = 0, for x =/= -3/2e^t = 2t = ln2
It is hard to express t in terms of x and vice versa.
參考: Physics king
收錄日期: 2021-04-19 21:19:50
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