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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/01.07.13.0001.01









  


  








Input Form





Derivative[2][w][z] + w[z] == 0 /; w[z] == Cos[z] && w[0] == 1 && Derivative[1][w][0] == 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "+", RowBox[List["w", "[", "z", "]"]]]], "\[Equal]", "0"]], " ", "/;", " ", RowBox[List[RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["Cos", "[", "z", "]"]]]], "\[And]", RowBox[List[RowBox[List["w", "[", "0", "]"]], "\[Equal]", "1"]], "\[And]", RowBox[List[RowBox[List[RowBox[List["w", "'"]], "[", "0", "]"]], "\[Equal]", "0"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msup> <mi> w </mi> <mi> &#8242;&#8242; </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <msup> <mi> w </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <cos /> <ci> z </ci> </apply> </apply> <apply> <eq /> <apply> <ci> w </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <ci> D </ci> <apply> <ci> w </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "+", RowBox[List["w", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["Cos", "[", "z", "]"]]]], "&&", RowBox[List[RowBox[List["w", "[", "0", "]"]], "\[Equal]", "1"]], "&&", RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "0", "]"]], "\[Equal]", "0"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29