Difference between revisions of "Jan Math 2008-12-05"

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(New page: == 4.1 d) == <math>y''+6x=0</math> = homogene = <math>y''=0</math> D.h. y zweimal differenziert ist 0, da kann y maximal x hoch zwei sein (Polynom). Homogene Lösung (allgemein) <math>y_h...)
 
Line 7: Line 7:
 
<math>y_h=ax^2+bx+c</math>
 
<math>y_h=ax^2+bx+c</math>
 
= spezielle Lösung =
 
= spezielle Lösung =
−
<math>y_sp''=-6x</math>
+
<math>y_{sp}''=-6x</math>
  
 
Einfach zweimal integrieren:
 
Einfach zweimal integrieren:
  
−
<math>y_sp'=-3x^2</math>
+
<math>y_{sp}'=-3x^2</math>
  
 
(kein +C, da man ja nur eine spezielle Lösung sucht!)
 
(kein +C, da man ja nur eine spezielle Lösung sucht!)
  
−
<math>y_sp=-x^3</math>
+
<math>y_{sp}=-x^3</math>
 
= Gesamtlösung =
 
= Gesamtlösung =
−
<math>y=y_sp+y_h</math><br/>
+
<math>y=y_{sp}+y_h</math><br/>
 
<math>y=-x^3+ax^2+bx+c</math>
 
<math>y=-x^3+ax^2+bx+c</math>
  
Line 27: Line 27:
 
<math>y_h=ax^2+bx+c</math>
 
<math>y_h=ax^2+bx+c</math>
 
= spezielle =
 
= spezielle =
−
<math>y_sp''=-6x+3</math><br/>
+
<math>y_{sp}''=-6x+3</math><br/>
−
<math>y_sp'=-3x^2+3x</math><br/>
+
<math>y_{sp}'=-3x^2+3x</math><br/>
−
<math>y_sp=-x^3+3/2 x^2</math>
+
<math>y_{sp}=-x^3+3/2 x^2</math>
 
= Gesamtlösung =
 
= Gesamtlösung =
−
<math>y=y_sp+y_h</math><br/>
+
<math>y=y_{sp}+y_h</math><br/>
 
<math>y=-x^3+3/2 x^2 +ax^2+bx+c</math><br/>
 
<math>y=-x^3+3/2 x^2 +ax^2+bx+c</math><br/>
 
Da a,b,c beliebig - im speziellen a - ist die allgemeine Lösung:
 
Da a,b,c beliebig - im speziellen a - ist die allgemeine Lösung:
  
 
<math>y=-x^3+ax^2+bx+c</math>
 
<math>y=-x^3+ax^2+bx+c</math>

Revision as of 08:01, 4 December 2008

4.1 d)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y''+6x=0}

homogene

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y''=0}

D.h. y zweimal differenziert ist 0, da kann y maximal x hoch zwei sein (Polynom). Homogene Lösung (allgemein) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_h=ax^2+bx+c}

spezielle Lösung

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_{sp}''=-6x}

Einfach zweimal integrieren:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_{sp}'=-3x^2}

(kein +C, da man ja nur eine spezielle Lösung sucht!)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_{sp}=-x^3}

Gesamtlösung

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=y_{sp}+y_h}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=-x^3+ax^2+bx+c}

(a,b,c beliebig)

4.1 e)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y''+6x-3=0}

homogene

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_h''=0}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_h=ax^2+bx+c}

spezielle

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_{sp}''=-6x+3}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_{sp}'=-3x^2+3x}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_{sp}=-x^3+3/2 x^2}

Gesamtlösung

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=y_{sp}+y_h}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=-x^3+3/2 x^2 +ax^2+bx+c}
Da a,b,c beliebig - im speziellen a - ist die allgemeine Lösung:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=-x^3+ax^2+bx+c}

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