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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[a,z] > Differential equations > Partial differential equations





http://functions.wolfram.com/01.05.13.0001.01









  


  








Input Form





a D[w[a, z], a] + z w[a, z] D[w[a, z], z] == 0 /; w[a, z] == Log[a, z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["a", " ", RowBox[List[SubscriptBox["\[PartialD]", "a"], RowBox[List["w", "[", RowBox[List["a", ",", "z"]], "]"]]]]]], "+", RowBox[List["z", " ", RowBox[List["w", "[", RowBox[List["a", ",", "z"]], "]"]], " ", RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["w", "[", RowBox[List["a", ",", "z"]], "]"]]]]]]]], "\[Equal]", "0"]], "/;", " ", RowBox[List[RowBox[List["w", "[", RowBox[List["a", ",", "z"]], "]"]], "\[Equal]", RowBox[List["Log", "[", RowBox[List["a", ",", "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> <mi> a </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msub> <mi> log </mi> <mi> a </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <partialdiff /> <bvar> <ci> a </ci> </bvar> <apply> <ci> w </ci> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> w </ci> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> w </ci> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> a </ci> <ci> z </ci> </apply> <apply> <log /> <logbase> <ci> a </ci> </logbase> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["a_"]]], RowBox[List["w", "[", RowBox[List["a_", ",", "z_"]], "]"]]]]]], "+", RowBox[List["z_", " ", RowBox[List["w", "[", RowBox[List["a_", ",", "z_"]], "]"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["w", "[", RowBox[List["a_", ",", "z_"]], "]"]]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", RowBox[List["a", ",", "z"]], "]"]], "\[Equal]", RowBox[List["Log", "[", RowBox[List["a", ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29