history "TutoriumMathe3Variationen":Projekt Einsparzähler

Revision history for TutoriumMathe3Variationen

Revision [71970]

Last edited on 2016-09-26 19:01:52 by Jorina Lossau

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-C(x)/x^2 + C'(x)/x + 1/x* C(x)/x = 5e^(-2x)
C'(x)=5xe^(-2x) integrieren !
C(x)=-5/2xe^(-2x)-5/4e^(-2x)+k
y=-5/2e^(-2x)-5/(4x)e^(-2x)+k/x=allgemeine Lösung
y(-0,5)=-5/2e^1-5/-2e^1+k/-0,5=-2k=-8
-> k=4
y=-5/2e^(-2x)-5/(4x)e^(-2x)+4/x

Revision [71969]

Edited on 2016-09-26 18:52:21 by Jorina Lossau

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y=C(x)/x -> y' = -C(x)/x^2 + C'(x)/x

Revision [71968]

Edited on 2016-09-26 18:50:34 by Jorina Lossau

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y'+(1/x)y=5e^(-2x)
y'+(1/x)y=0->(dy)/(dx)+(1/x)y=0->(dy)/y=-(dx)/x
ln Betrag von y = -ln Betrag von x + Cgestrichen -> ln Betrag von xy = Cgestrichen -> xy = +-e^C gestrichen = C

Revision [58985]

Edited on 2015-09-07 10:42:53 by Jorina Lossau

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Revision [58984]

Edited on 2015-09-07 10:41:03 by Jorina Lossau

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spezielle Lösung:
{{image url="Konstante8.jpg" width="400" class="left"}}

Revision [58983]

Edited on 2015-09-07 10:33:42 by Jorina Lossau

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~~{{image url="Konstante7.jpg" width="200" class="left"}}~~

Revision [58980]

Edited on 2015-09-07 10:26:50 by Jorina Lossau

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Anfangsbedingung:
{{image url="Konstante7.jpg" width="200" class="left"}}

Revision [58978]

Edited on 2015-09-07 10:19:25 by Jorina Lossau

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{{image url="Konstante6.jpg" width="200" class="left"}} = allgemeine Lösung

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~~{{image url="Konstante6.jpg" width="250" class="left"}}~~

Revision [58976]

Edited on 2015-09-07 10:18:10 by Jorina Lossau

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in Ansatz einsetzen:
{{image url="Konstante6.jpg" width="250" class="left"}}

Revision [58975]

Edited on 2015-09-07 10:15:54 by Jorina Lossau

No Differences

Revision [58974]

Edited on 2015-09-07 10:14:21 by Jorina Lossau

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einfache DGL für C(x)
{{image url="Konstante5.jpg" width="250" class="left"}}

Revision [58972]

Edited on 2015-09-07 10:00:45 by Jorina Lossau

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~~{{image url="Konstante4.jpg" width="350" class="left"}}~~

Revision [58971]

Edited on 2015-09-07 09:59:04 by Jorina Lossau

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einsetzen:
{{image url="Konstante4.jpg" width="350" class="left"}}

Revision [58970]

Edited on 2015-09-07 09:54:59 by Jorina Lossau

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~~{{image url="Konstante3.jpg" width="450" class="left"}}~~

Revision [58969]

Edited on 2015-09-07 09:53:29 by Jorina Lossau

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homogene Lösung: yH = C/X
Ansatz:
{{image url="Konstante3.jpg" width="450" class="left"}}

Revision [58961]

Edited on 2015-09-07 09:11:23 by Jorina Lossau

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~~{{image url="Konstante2.jpg" width="130" class="left"}}~~

Revision [58960]

Edited on 2015-09-07 09:09:42 by Jorina Lossau

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zug. hom. DGL:
{{image url="Konstante2.jpg" width="130" class="left"}}

Revision [58959]

Edited on 2015-09-07 08:59:38 by Jorina Lossau

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~~{{image url="Konstante1.jpg" width="300" class="center"}}~~

Revision [58958]

Edited on 2015-09-07 08:58:17 by Jorina Lossau

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**Beispiel: **
Anfangsbedingung: y(-5) = -8
{{image url="Konstante1.jpg" width="300" class="center"}}

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~~{{image url="Konstante1.jpg" width="600" class="center"}}~~

Revision [58957]

Edited on 2015-09-07 08:54:22 by Jorina Lossau

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Revision [58343]

Edited on 2015-08-27 10:44:31 by Jorina Lossau

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Revision [58340]

Edited on 2015-08-27 10:23:46 by Jorina Lossau

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Revision [58339]

Edited on 2015-08-27 09:46:56 by Jorina Lossau

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{{files}}
|=|{color:#00386a; background-color: #E0E0E0; width: 700px} Vorgehensweise||
|=|{background-color: #FFFFFF; width: 700px}
Diese Methode bietet sich für lineare inhomogene DGL mit konstanten Koeffizienten an, wenn die Störfunktion nicht auf einen einfachen Ansatz für eine partikuläre Lösung hinweist. Darüber hinaus ist die Methode auch oft für lineare homogene DGL mit konstanten Koeffizienten geeignet.
Im einfachsten Fall einer inhomogenen DGL erster Ordnung wird wie folgt vorgegangen:
Die freie Konstante der allgemeinen Lösung C der zugehörigen homogenen DGL wird als Funktion C (x) von x betrachtet. Durch Einsetzen in die inhomogene DGL erhält man eine einfachere DGL für C (x), welches dann bestimmt werden kann.
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Revision [43698]

Edited on 2014-08-27 10:06:15 by Jorina Lossau

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Revision [43697]

The oldest known version of this page was created on 2014-08-27 09:42:50 by Jorina Lossau