Revision history for TutoriumMathe3L8
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{{image url="Konstante38.jpg" width="200" class="left"}}
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y(0) = K - 1 = 2 --> K = 3
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**Var. d. Konst.:** C ist nun eine Funktion von x
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**1.6.6**
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**1.6.6**
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u = x, u' = 1
v' = cos(x), v = sin(x)
C = xsin(x) + cos(x) + K
--> y = (xsin(x) + cos(x) + K) cosx) = allgemeine Lösung
y(0) = 1 + K = -2
K = -3
--> y = (xsin(x) + cos(x) -3) cos(x) = spezielle Lösung
v' = cos(x), v = sin(x)
C = xsin(x) + cos(x) + K
--> y = (xsin(x) + cos(x) + K) cosx) = allgemeine Lösung
y(0) = 1 + K = -2
K = -3
--> y = (xsin(x) + cos(x) -3) cos(x) = spezielle Lösung
Additions:
{{image url="Konstante31.jpg" width="300" class="left"}}
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**Var. d. Konst.:** C ist nun Funktion von x
y = Ccos(x)
y'=C'cos(x)-Csin(x)
y = Ccos(x)
y'=C'cos(x)-Csin(x)
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{{image url="Konstante31.jpg" width="250" class="left"}}
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**zug. hom.:**
sin(x)y + cos(x)y' = 0
sin(x)y + cos(x)y' = 0
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y(0) = -2
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**1.6.5**
**1.6.5**
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y(0) = K = 0
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**lin. Substitution:**
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**Var. der Konst.:**
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y' + 5y = 0
**charakt. Gl.:**
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**charakt. Gl.:**
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**1.6.4**
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**1.6.4**
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K = 4
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**Var. d. Konst.:**
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**charakt. Gl.: **
{{image url="Konstante18.jpg" width="250" class="left"}}
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**zug. hom.: **
y' +2y = 0
y' +2y = 0
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**1.6.3**
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1.6.3
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y(0) = 25
25 = K - 10 --> K = 35
{{image url="Konstante16.jpg" width="300" class="left"}}
25 = K - 10 --> K = 35
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**mit part. Integration:**
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**in inhom. DGL:**
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in inhom. DGL:
{{image url="Konstante13.jpg" width="180" class="left"}}
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**char. Gleichung: **
{{image url="Konstante10jpg" width="300" class="left"}}
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y' + 2y = 0
char. Gleichung:
char. Gleichung:
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= spezielle Lösung
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= allgemeine Lösung
= allgemeine Lösung
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**in DGL:**
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**Variation der Konst.:**
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Variation der Konst.:
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**zug. hom.:**
{{image url="Konstante2.jpg" width="250" class="left"}}
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||**1.6 Lösen Sie die folgenden Differentialgleichungenmit der Methode der „Variation der Konstanten“.**
{{image url="Konstante1.jpg" width="250" class="left"}}
{{image url="Konstante1.jpg" width="250" class="left"}}
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{{image url="Konstante1.jpg" width="650" class="center"}}
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{{files}}
||1.6 Lösen Sie die folgenden Differentialgleichungenmit der Methode der „Variation der Konstanten“.
{{image url="Konstante1.jpg" width="650" class="center"}}
||
||1.6 Lösen Sie die folgenden Differentialgleichungenmit der Methode der „Variation der Konstanten“.
{{image url="Konstante1.jpg" width="650" class="center"}}
||
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