integer - how to assing coefficients both positive and real using dsolve -



integer - how to assing coefficients both positive and real using dsolve -

so want solve these equation

fullsimplify[dsolve[{il''[t] + il[t]/(c*l) == vc[t]/(c*l*r), c*vc''[t] + vc'[t]/r + vc[t]/l == vin/l}, {il[t], vc[t]},t] {{c, l, r} \[element] reals && c >= 0 && l >= 0 && r >= 0}]

symbolically , want assing r,l , c positive real integer solution comes imaginer part there other way using dsolve

assuming variable greater 0 implies variable real. integer not help in problem.

if r, l , c greater 0 , less infinity multiplying both sides eliminate denominators speed , simplify calculation in mathematica.

if had simple initial conditions simpler , perhaps faster.

this gets rid of imaginary parts in vc , imaginary parts in il

simplify[exptotrig[dsolve[{ il''[t]*c*l*r + il[t]*r == vc[t], vc''[t]*c*l*r + vc'[t]*l + vc[t]*r == vin*r}, {il[t], vc[t]}, t]], l > 0 && c > 0 && r > 0]

and fast.

fullsimplify much slower, if wait result is

{{il[t] -> (e^(-(t/(2 c r))) (l sqrt[l - 4 c r^2] (c[3] + c r c[4]) cosh[(sqrt[1 - (4 c r^2)/l] t)/(2 c r)] + e^(t/(2 c r)) sqrt[l - 4 c r^2] (l vin - l (-r c[1] + c[3] + c r c[4]) cos[t/sqrt[c l]] + sqrt[c l] r (l c[2] + c[3]) sin[t/sqrt[c l]]) + sqrt[l] ((l - 2 c r^2) c[3] + c l r c[4]) sinh[(sqrt[1 - (4 c r^2)/l] t)/(2 c r)]))/(l r sqrt[l - 4 c r^2]), vc[t] -> ((l - 4 c r^2) vin + e^(-(t/(2 c r))) ((l - 4 c r^2) c[3] cosh[(sqrt[1 - (4 c r^2)/l] t)/(2 c r)] + sqrt[l (l - 4 c r^2)] (c[3] + 2 c r c[4]) sinh[(sqrt[1 - (4 c r^2)/l] t)/(2 c r)]))/(l - 4 c r^2)}}

depending on whether or not l greater or equal 4 c r^2 there more potential complex values in result have farther simplified real result, 1 way or other.

integer wolfram-mathematica differential-equations

Comments

Post a Comment

Popular posts from this blog

xslt - DocBook 5 to PDF transform failing with error: "fo:flow" is missing child elements. Required content model: marker* -

xslt - DocBook 5 to PDF transform failing with error: "fo:flow" is missing child elements. Required content model: marker* - i've inherited doc publishing process takes docbook , builds html , pdf output, using apache fop both. project had been started, never completed. lots of tweaking, i've able of doc sets build (20+), except handful, , fail severe code 1 of these 2 conditions: "fo:flow" missing kid elements. required content model: marker* "fo:block" not valid kid of "fo:root" the xml output comes out of docbook , docbook-fop checks out well-formed. the fop error in 1 book, "endecagloss", example, points end of string: <fo:flow flow-name="xsl-region-body" start-indent="4pc" end-indent="0pt"/> here’s log output in case: [java] severe: javax.xml.transform.transformerexception: file:/scratch/publishing/hudson/jobs/build-main-endeca-documentation/workspace/serverdoc/w...
Read more

mediawiki - How do I insert tables inside infoboxes on Wikia pages? -

mediawiki - How do I insert tables inside infoboxes on Wikia pages? - i want insert tables in infoboxes. example, have proteinbox i've developed using infobox template (http://health-and-medicine.wikia.com/wiki/template:proteinbox), , fasta field big fit comfortably in proteinbox. hence collapsible table within box. this tried: {{infobox | row 1 = {| class = "mw-collapsible mw-collapsed wikitable" |- | <!-- table content --> |} }} your problem is, putting nested table within template. pipe characters ( | ) in table syntax collides pipe usage in templates. the commonly used hack around create template called template:! , containing pipe character, , utilize when need set tables, parser functions or other stuff using pipe characters, within templates. table (with every | replaced {{!}} ): {{{!}} {{!}}- {{!}} a1 {{!}} b1 {{!}}- {{!}} a2 {{!}} b2 {{!}}} ...the equivalent of {| |- | a1 | b1 |- | a2 | b2 |} furthermore, hav...
Read more

Local Service User Logged into Windows -

Local Service User Logged into Windows - i created windows service tracks app server user connected through load balancer. it retrieves user logged windows on machine, cross references active directory (ad) business relationship homecoming first name, lastly name , e-mail (for notification through website created project) there 1 scheme on network users remote system, vista system, reason returning values "local service" logged machine, it's weird , security guys impossible "local service" business relationship logged windows. here how user logged windows managementscope ms = new managementscope("\\\\.\\root\\cimv2"); objectquery query = new objectquery("select * win32_computersystem"); managementobjectsearcher searcher = new managementobjectsearcher(ms, query); foreach (managementobject mo in searcher.get()) { _username = mo["username"].tostring(); } // remove domain part username string[] usernameparts = _...
Read more