Revision as of 08:08, 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}

4.1 f)

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''+12x^2-4x=1}
- homogene (wie schon zwei Mal) -
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}
- spezeille -
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}''=-12x^2+4x+1}
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}'=-4x^2+2x^2+x}
<math>y_{sp}=-

@@ Line 1: / Line 1: @@
 = 4.1 d) =
-<math>y''+6x=0</math>
+<math>y''+6x=0</math><br/>
-- homogene -
+- homogene -<br/>
-<math>y''=0</math>
+<math>y''=0</math><br/>
+D.h. y zweimal differenziert ist 0, da kann y maximal x hoch zwei sein (Polynom). Homogene Lösung (allgemein)<br/>
-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><br/>
-<math>y_h=ax^2+bx+c</math>
+- spezielle Lösung -<br/>
-- spezielle Lösung -
+<math>y_{sp}''=-6x</math><br/>
-<math>y_{sp}''=-6x</math>
+Einfach zweimal integrieren:<br/>
+<math>y_{sp}'=-3x^2</math><br/>
-Einfach zweimal integrieren:
+(kein +C, da man ja nur eine spezielle Lösung sucht!)<br/>
+<math>y_{sp}=-x^3</math><br/>
-<math>y_{sp}'=-3x^2</math>
+- Gesamtlösung -<br/>
-(kein +C, da man ja nur eine spezielle Lösung sucht!)
-<math>y_{sp}=-x^3</math>
-- Gesamtlösung -
 <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><br/>
 (a,b,c beliebig)
 = 4.1 e) =
-<math>y''+6x-3=0</math>
+<math>y''+6x-3=0</math><br/>
-- homogene -
+- homogene -<br/>
 <math>y_h''=0</math><br/>
-<math>y_h=ax^2+bx+c</math>
+<math>y_h=ax^2+bx+c</math><br/>
-- spezielle -
+- spezielle -<br/>
 <math>y_{sp}''=-6x+3</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><br/>
-- Gesamtlösung -
+- Gesamtlösung -<br/>
 <math>y=y_{sp}+y_h</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 (diesmal ein 'anderes' a):
+Da a,b,c beliebig - im speziellen a - ist die allgemeine Lösung (diesmal ein 'anderes' a):<br/>
+<math>y=-x^3+ax^2+bx+c</math><br/>
-<math>y=-x^3+ax^2+bx+c</math>
+= 4.1 f) =
+<math>y''+12x^2-4x=1</math><br/>
+- homogene (wie schon zwei Mal) -<br/>
+<math>y_h=ax^2+bx+c</math><br/>
+- spezeille -<br/>
+<math>y_{sp}''=-12x^2+4x+1</math><br/>
+<math>y_{sp}'=-4x^2+2x^2+x</math><br/>
+<math>y_{sp}=-

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

Revision as of 08:08, 4 December 2008

4.1 d)

4.1 e)

4.1 f)

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