/sci/ - Science & Math

[math] y'(t) = A(t)\, y(t) +B(t) [/math]

with, in, your case, [math] A(t)=-a [/math] and [math] B(t) = b\, u(t)-c\, d(t) [/math].

Now

[math] y(t) = S(t,0) y(0) + \int_0^t S(t,s) \, B(s) \, ds [/math]

where [math] S(t,s) = e^{I(t)-I(s)} [/math], where [math] I(t) = \int_0^t A(s) \, ds. [/math] In your case, A is constant, which makes this quite simple.

Here [math] B [/math] plays the role of a force, which you might be calling an input.

Know the calculus

>buy tight clothes
>get right man
>have money

who's the dumb one now.

>>8108294
You lack information if you are tempted to put Feynman above Neumann.

All those guys, Einstein, Neumann, and Feynman in particular were extroverts and thus they are more in out mind.
Dirac was super smart but an autistic introvert and so people don't know his name.

Continuing with the Russians I posted in >>8107202, consider
https://en.wikipedia.org/wiki/Nikolay_Bogolyubov
He did a fuckload of stuff, but of course he doesn't have the exposure of a Feynman.

https://youtu.be/oJG8cmlkPuw

>>7984196
>how so?
Because the functions from N to {0,1} are already not enumerable. That is to say, the function space N->{0,1}, which is in bijection with the powerset of N, is uncountably infinite.
And in fact, postulating that it's just as big as R (continuum hypothesis) is consistent with any standard set theory.

>so why can't we come up with any rules or any objects beyond these two countable and uncountable arenas?
You can do math that's not sets with cardinalities - then you cannot express those notions. But "the problem" (second order) logic itself is already a type/set theory, so as soon as you make your reasoning modalities strong enough, you get that stuff back.

Besides, uncountable is a catch-all term and there are infinities far beyond the cardinalities of R^n, see e.g.
http://cantorsattic.info/Cantor's_Attic