Derivative[1][w][z] - (Derivative[1][g][z]/(2 g[z]) + Derivative[1][h][z]/h[z]) w[z] == 0 /; w[z] == Subscript[c, 1] h[z] Sqrt[g[z]]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], RowBox[List["2", RowBox[List["g", "[", "z", "]"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["h", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], RowBox[List["h", "[", "z", "]"]]]]], ")"]], RowBox[List["w", "[", "z", "]"]]]]]], "\[Equal]", "0"]], "/;", " ", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[SubscriptBox["c", "1"], RowBox[List["h", "[", "z", "]"]], SqrtBox[RowBox[List["g", "[", "z", "]"]]], " "]]]]]]]]

<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> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mtext> </mtext> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> h </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msqrt> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> h </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <ci> h </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> h </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], RowBox[List["2", " ", RowBox[List["g", "[", "z_", "]"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["h", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], RowBox[List["h", "[", "z_", "]"]]]]], ")"]], " ", RowBox[List["w", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[SubscriptBox["c", "1"], " ", RowBox[List["h", "[", "z", "]"]], " ", SqrtBox[RowBox[List["g", "[", "z", "]"]]]]]]]]]]]]]

2007-05-02