Difference between revisions of "Jan Math 2008-12-05"
(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...) |
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| 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> | + | <math>y_{sp}''=-6x</math> |
Einfach zweimal integrieren: | Einfach zweimal integrieren: | ||
| − | <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> | + | <math>y_{sp}=-x^3</math> |
= Gesamtlösung = | = Gesamtlösung = | ||
| − | <math>y= | + | <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> | + | <math>y_{sp}''=-6x+3</math><br/> |
| − | <math> | + | <math>y_{sp}'=-3x^2+3x</math><br/> |
| − | <math> | + | <math>y_{sp}=-x^3+3/2 x^2</math> |
= Gesamtlösung = | = Gesamtlösung = | ||
| − | <math>y= | + | <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)
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}