Derivative[1][w][z]^3 - w[z]^2 (w[z] - a)^2 == 0 /; w[z] == a/2 + (27/16) WeierstrassPPrime[z/2, {0, (-(64/729)) a^2}]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]"], "[", "z", "]"]], "3"], "-", RowBox[List[SuperscriptBox[RowBox[List["w", "[", "z", "]"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["w", "[", "z", "]"]], "-", "a"]], ")"]], "2"]]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["a", "2"], "+", RowBox[List[FractionBox["27", "16"], " ", RowBox[List["WeierstrassPPrime", "[", RowBox[List[FractionBox["z", "2"], ",", RowBox[List["{", RowBox[List["0", ",", RowBox[List[RowBox[List["-", FractionBox["64", "729"]]], SuperscriptBox["a", "2"]]]]], "}"]]]], "]"]]]]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mrow> <msup> <mi> w </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> - </mo> <mrow> <msup> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 27 </mn> <mn> 16 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> &#8472; </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mrow> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mn> 0 </mn> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 64 </mn> <mn> 729 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> w </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 27 <sep /> 16 </cn> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> &#8472; </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 64 <sep /> 729 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "3"], "-", RowBox[List[SuperscriptBox[RowBox[List["w", "[", "z_", "]"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["w", "[", "z_", "]"]], "-", "a_"]], ")"]], "2"]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["a", "2"], "+", RowBox[List[FractionBox["27", "16"], " ", RowBox[List["WeierstrassPPrime", "[", RowBox[List[FractionBox["z", "2"], ",", RowBox[List["{", RowBox[List["0", ",", RowBox[List[FractionBox["1", "729"], " ", RowBox[List["(", RowBox[List["-", "64"]], ")"]], " ", SuperscriptBox["a", "2"]]]]], "}"]]]], "]"]]]]]]]]]]]]]]

2001-10-29