Question: Given d^2 f(t) / dt^2 = d( d(f(t))/dt )/dt = g(t), where g(t)
is known, but f(t) is unknown, what is the complete solution of
f(t) in terms of g(t) ?
數學物理證明題(2)
2007-10-11 7:24 am
回答 (1)
2007-10-11 8:22 pm
✔ 最佳答案
d2 f(t)/dt2 = g(t) f(t)=∫∫g(t)dt dt
Let G(t)= ∫g(t)dt, where d( G(t) + c )/dt = g(t), for all c, c1, c2 …… is a constant. And let F(t)= ∫G(t)dt
f(t)=∫ ( G(t)+ c ) dt = F(t) + ct + c1
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