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Mathematica Notation

Traditional Notation

Elementary Functions > Power[z,a] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself > With respect to a




Input Form

Derivative[1][w][a] - Log[z] w[a] == 0 /; w[a] == z^a && w[1] == z

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "a", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "z", "]"]], RowBox[List["w", "[", "a", "]"]]]]]], "\[Equal]", "0"]], "/;", " ", RowBox[List[RowBox[List[RowBox[List["w", "[", "a", "]"]], "\[Equal]", SuperscriptBox["z", "a"]]], "\[And]", RowBox[List[RowBox[List["w", "[", "1", "]"]], "\[Equal]", "z"]]]]]]]]

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> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <msup> <mi> z </mi> <mi> a </mi> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <partialdiff /> <bvar> <ci> a </ci> </bvar> <apply> <ci> w </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> z </ci> </apply> <apply> <ci> w </ci> <ci> a </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> w </ci> <ci> a </ci> </apply> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> </apply> <apply> <eq /> <apply> <ci> w </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

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