[University Differential Equations and Electrical Circuits] Including an additional constant in the solution of a first-order linear ODE

2022.01.21 16:34 TheEpicPineapple [University Differential Equations and Electrical Circuits] Including an additional constant in the solution of a first-order linear ODE

I am learning about RL and RC circuit response right now, and much of that is solving linear 1st order ODEs. The solution is usually easily found by using the Integrating Factor, but I am a little confused about something. As far as I know, 1st order ODEs require only one constant to find a general solution. But it appears that if you want to specify behavior both at t=0 and t=∞, then you can actually use TWO constants. For example:
Initial Condition for current through an inductor: -4.00mA (solved through mesh current by setting the inductor to a short circuit)
Final Condition for current through an inductor: 1.00mA (solved for the same way) Let's just say the time constant is 0.1
The solution for the current i(t) is then:
i(t) = 1 - 5e-10t. By inspection, one can see that the behavior at t=0 (initial state) is satisfied because i(0) = -4 and the behavior at t=∞ (final state) is satisfied because i(∞) = 1
This suggests that if I have a first-order homogeneous linear ODE with constant coefficients
y'(t) + ky = 0
the solution is actually y(t) = Ae-kt + C where C describes the asymptotic behavior at t=∞ and A + C describes the behavior at t=0
If you take the derivative of this equation, the C goes away anyway...so then why did I learn that 1st-order ODEs only require one constant (and that adding another constant is in fact opening me up to the possibility of overdetermination)? Why can I easily add a constant to describe the behavior at ∞ if I so desire without messing up the form of the original equation? I thought there was only supposed to be one constant of integration introduced. Could this be a case of linear superposition that I am kinda being dim about? In short, what is the reason (please not just by inspection) that I can just say "+ C" in the general solution without messing up the original form of the differential equation? Thanks!
submitted by TheEpicPineapple to learnmath [link] [comments]


2022.01.21 16:34 shrimpnwine 2022 DCSB OR Progress!

2022 DCSB OR Progress! submitted by shrimpnwine to ToyotaTacoma [link] [comments]


2022.01.21 16:34 Bonus1Fact [News Shorts] Giants hiring Joe Schoen as new general manager ¦ NY Post on Rumble

submitted by Bonus1Fact to NewsShorts [link] [comments]


2022.01.21 16:34 dragonslayr56 First time doing mild steel tig r joints criticism welcome

First time doing mild steel tig r joints criticism welcome submitted by dragonslayr56 to Welding [link] [comments]


2022.01.21 16:34 Apprehensive-Oil5249 Pavia/ADA Exchange????

Just so I'm not going crazy here but despite the issues with Sundae Swap and Nami and whatnot.....did anyone else catch the exchange rate of Pavia for ADA?????
submitted by Apprehensive-Oil5249 to PaviaMetaverse [link] [comments]


2022.01.21 16:34 5igorsk Так выглядела транспортировка резервуаров, разработанных "Криогенмашем" для комплекса криогенных систем хранения и заправки жидкими водородом и кислородом для ракетной системы "Энергия" с космическим кораблем многоразового использования "Буран".

Так выглядела транспортировка резервуаров, разработанных submitted by 5igorsk to Tay_5 [link] [comments]


2022.01.21 16:34 ASICmachine Pulling prices from CMC to google sheets but I need more accurate prices (x-post from /r/Cryptocurrency)

submitted by ASICmachine to CryptoCurrencyClassic [link] [comments]


2022.01.21 16:34 Swittenbrh Help

I dont understand why just why Personal possesives, personal Pronouns and Adjectives depends on the Case, how am i supposed to know whether we use the first form of the word or with the changed one based ln thé case? I need a link please
submitted by Swittenbrh to Polish [link] [comments]


2022.01.21 16:34 TheOnlyDrifter Server "uptime"

Anyone host or rent a server do you known if the server keeps running when no one is online?
Looking at renting one at 4players.com I think was the one was going with
And I was just wondering if the server keeps running thru the days if no one is in the server.
submitted by TheOnlyDrifter to projectzomboid [link] [comments]


2022.01.21 16:34 Stickboi_85 My home base feel free to judge and comment ideas or concerns

My home base feel free to judge and comment ideas or concerns submitted by Stickboi_85 to Minecraftbuilds [link] [comments]


2022.01.21 16:34 jennifeet99 I’ll be free once I’m done with my studies💋

I’ll be free once I’m done with my studies💋 submitted by jennifeet99 to FootFetishExperiences [link] [comments]


2022.01.21 16:34 NoEnergy1035 먹튀감정사 https://verification.kr/ 먹튀검증,먹튀사이트,먹튀검증사이트,먹튀검증커뮤니티,토토사이트,카지노사이트,먹튀,먹튀제보,먹튀신고,먹튀검증업체,파워볼사이트,토토먹튀,카지노먹튀,파워볼먹튀

먹튀감정사 https://verification.k 먹튀검증,먹튀사이트,먹튀검증사이트,먹튀검증커뮤니티,토토사이트,카지노사이트,먹튀,먹튀제보,먹튀신고,먹튀검증업체,파워볼사이트,토토먹튀,카지노먹튀,파워볼먹튀 https://preview.redd.it/cjrj6rtff3d81.jpg?width=1000&format=pjpg&auto=webp&s=cfb1ede4349a653a789dcaf88550f4e9ed76ae82
https://preview.redd.it/w7lhsorff3d81.jpg?width=1000&format=pjpg&auto=webp&s=0bed8fd04b174846f727b9773d1be32776342e12
https://preview.redd.it/8o96mmrff3d81.jpg?width=1000&format=pjpg&auto=webp&s=24e13d809c37bd244c6e067fe2eddf551809fdaf
https://preview.redd.it/ivtwogrff3d81.jpg?width=1000&format=pjpg&auto=webp&s=fbb57326f2fd676a60cb8a3131d2f9c5578b9079
https://preview.redd.it/axs6dnrff3d81.jpg?width=1000&format=pjpg&auto=webp&s=cc0cccac2ce5e8a0c637f4819dcc6978df439c17
https://preview.redd.it/hquarjrff3d81.jpg?width=1000&format=pjpg&auto=webp&s=fc72fc9d1cbc7d7517edb993a46dc8a130ed9b12
https://preview.redd.it/8wb7ljrff3d81.jpg?width=1000&format=pjpg&auto=webp&s=6e77ea1f232d13f69c4d2b515986befed2882283
먹튀감정사 https://verification.k
먹튀검증,먹튀사이트,먹튀검증사이트,먹튀검증커뮤니티,토토사이트,카지노사이트,먹튀,먹튀제보,먹튀신고,먹튀검증업체,파워볼사이트,토토먹튀,카지노먹튀,파워볼먹튀
submitted by NoEnergy1035 to redditkorea [link] [comments]


2022.01.21 16:34 Azami13 D - Fantasy Inspiration (Maria Amanda)

D - Fantasy Inspiration (Maria Amanda) submitted by Azami13 to Kibbe [link] [comments]


2022.01.21 16:34 AsterTheArtist [FANART] Found my old ink drawing of some Josuke panels from Diamond is Unbreakable. It looks good when scanned so the materials were just standing there... menacingly

[FANART] Found my old ink drawing of some Josuke panels from Diamond is Unbreakable. It looks good when scanned so the materials were just standing there... menacingly submitted by AsterTheArtist to StardustCrusaders [link] [comments]


2022.01.21 16:34 Salt-Contribution-62 What would you ask a six year old?

submitted by Salt-Contribution-62 to AskReddit [link] [comments]


2022.01.21 16:34 R_Jay101 At what income did you start feeling financially stable?

Obviously, everyones circumstances are different (e.g. living alone compared to living with a partner with 3 kids).
Was there a point where you werent stressing as much about money?
submitted by R_Jay101 to UKPersonalFinance [link] [comments]


2022.01.21 16:34 Kind-Dragonfly-2247 Will I survive ME?

Hi! I’m currently a MGT freshie who plans to shift to ME next school year. I just have some questions in mind about the course:

  1. Is ME really as difficult as most people describe it? (Especially for the Math subs)
  2. How is ME’s environment with your fellow students? Are students competitive?
  3. Do you still have a “life” in ME? Like having time for orgs and other extracurriculars?
submitted by Kind-Dragonfly-2247 to ADMU [link] [comments]


2022.01.21 16:34 Positive_Support8877 College readiness survey (NYC high school students & 10th-12th graders only)

College readiness survey (NYC high school students & 10th-12th graders only) submitted by Positive_Support8877 to APResearch [link] [comments]


2022.01.21 16:34 RedMystical As a rock/metalhead, I just recently acquired these vinyls. Am I a fan yet?

As a rock/metalhead, I just recently acquired these vinyls. Am I a fan yet? submitted by RedMystical to chvrches [link] [comments]


2022.01.21 16:34 Comfortable_Arm8078 so many based alphas among this cringe sub

so many based alphas among this cringe sub submitted by Comfortable_Arm8078 to shitposting [link] [comments]


2022.01.21 16:34 ntommy25 Please don’t hate me for making this…

Please don’t hate me for making this… submitted by ntommy25 to Patriots [link] [comments]


2022.01.21 16:34 CheeseIsGrossGoBears “Hey I’m open!” Can I evaluate the floor first? Geez and has anyone heard of off ball screens? “Bro just pass come on”

“Hey I’m open!” Can I evaluate the floor first? Geez and has anyone heard of off ball screens? “Bro just pass come on” submitted by CheeseIsGrossGoBears to NBA2k [link] [comments]


2022.01.21 16:34 me242sch Thank you Captain! @Good_Joker_20

Thank you Captain! @Good_Joker_20 submitted by me242sch to WoWs_Legends [link] [comments]


2022.01.21 16:34 ImmediateAttention46 orange stink nft

submitted by ImmediateAttention46 to NFTExchange [link] [comments]


2022.01.21 16:34 jookco Death - Obituary : Louie Anderson, St. Paul-native & Emmy-winning comedian, passed away today. In 1985, @MPR's Beth Friend discussed with Anderson his social work & comedy careers, his comedic inspirations, & his burgeoning stardom. Listen to the segment in the MPR Archive: Click link to read ful...

submitted by jookco to DeathObituaries [link] [comments]


http://monibabyshop.ru