Difference between revisions of "Jan Math 2008-12-05"
| Line 1: | Line 1: | ||
| − | + | = 4.1 d) = | |
<math>y''+6x=0</math> | <math>y''+6x=0</math> | ||
| − | + | - homogene - | |
<math>y''=0</math> | <math>y''=0</math> | ||
D.h. y zweimal differenziert ist 0, da kann y maximal x hoch zwei sein (Polynom). Homogene Lösung (allgemein) | D.h. y zweimal differenziert ist 0, da kann y maximal x hoch zwei sein (Polynom). Homogene Lösung (allgemein) | ||
<math>y_h=ax^2+bx+c</math> | <math>y_h=ax^2+bx+c</math> | ||
| − | + | - spezielle Lösung - | |
<math>y_{sp}''=-6x</math> | <math>y_{sp}''=-6x</math> | ||
| Line 16: | Line 16: | ||
<math>y_{sp}=-x^3</math> | <math>y_{sp}=-x^3</math> | ||
| − | + | - 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> | ||
(a,b,c beliebig) | (a,b,c beliebig) | ||
| − | + | = 4.1 e) = | |
<math>y''+6x-3=0</math> | <math>y''+6x-3=0</math> | ||
| − | + | - homogene - | |
<math>y_h''=0</math><br/> | <math>y_h''=0</math><br/> | ||
<math>y_h=ax^2+bx+c</math> | <math>y_h=ax^2+bx+c</math> | ||
| − | + | - 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 - | |
<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 (diesmal ein 'anderes' a): |
<math>y=-x^3+ax^2+bx+c</math> | <math>y=-x^3+ax^2+bx+c</math> | ||
Revision as of 08:03, 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 (diesmal ein 'anderes' a):
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}