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   http://functions.wolfram.com/01.06.13.0009.01
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    Derivative[2][w][z] - ((2 Derivative[1][h][z])/h[z] + 
     Derivative[2][g][z]/Derivative[1][g][z]) Derivative[1][w][z] + 
   (Derivative[1][g][z]^2 + (Derivative[1][h][z] Derivative[2][g][z])/
      (h[z] Derivative[1][g][z]) + (2 Derivative[1][h][z]^2)/h[z]^2 - 
     Derivative[2][h][z]/h[z]) w[z] == 0 /; 
 w[z] == Subscript[c, 1] h[z] Cos[g[z]] + Subscript[c, 2] h[z] Sin[g[z]] 
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   Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List[SuperscriptBox["h", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], RowBox[List["h", "[", "z", "]"]]], "+", FractionBox[RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]]], ")"]], RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "2"], "+", FractionBox[RowBox[List[RowBox[List[SuperscriptBox["h", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], RowBox[List[RowBox[List["h", "[", "z", "]"]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List[SuperscriptBox["h", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "2"]]], SuperscriptBox[RowBox[List["h", "[", "z", "]"]], "2"]], "-", FractionBox[RowBox[List[SuperscriptBox["h", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], RowBox[List["h", "[", "z", "]"]]]]], ")"]], RowBox[List["w", "[", "z", "]"]]]]]], "\[Equal]", "0"]], " ", "/;", " ", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], RowBox[List["h", "[", "z", "]"]], RowBox[List["Cos", "[", RowBox[List["g", "[", "z", "]"]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], RowBox[List["h", "[", "z", "]"]], RowBox[List["Sin", "[", RowBox[List["g", "[", "z", "]"]], "]"]]]]]]]]]]]]]] 
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   <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> ′′ </mi>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> - </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mfrac>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> h </mi>  <mo> ′ </mo>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mi> h </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mfrac>  <mo> + </mo>  <mfrac>  <mrow>  <msup>  <mi> g </mi>  <mi> ′′ </mi>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mrow>  <msup>  <mi> g </mi>  <mo> ′ </mo>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> w </mi>  <mo> ′ </mo>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <msup>  <mrow>  <msup>  <mi> g </mi>  <mo> ′ </mo>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  <mo> + </mo>  <mfrac>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <msup>  <mi> h </mi>  <mo> ′ </mo>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mrow>  <msup>  <mrow>  <mi> h </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mfrac>  <mo> + </mo>  <mfrac>  <mrow>  <mrow>  <msup>  <mi> h </mi>  <mo> ′ </mo>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> g </mi>  <mi> ′′ </mi>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mrow>  <mi> h </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> g </mi>  <mo> ′ </mo>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  <mo> - </mo>  <mfrac>  <mrow>  <msup>  <mi> h </mi>  <mi> ′′ </mi>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mrow>  <mi> h </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> w </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo>  </mo>  <mn> 0 </mn>  </mrow>  <mo> /; 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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List[SuperscriptBox["h", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], RowBox[List["h", "[", "z_", "]"]]], "+", FractionBox[RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "2"], "+", FractionBox[RowBox[List[RowBox[List[SuperscriptBox["h", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], RowBox[List[RowBox[List["h", "[", "z_", "]"]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List[SuperscriptBox["h", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "2"]]], SuperscriptBox[RowBox[List["h", "[", "z_", "]"]], "2"]], "-", FractionBox[RowBox[List[SuperscriptBox["h", "\[Prime]\[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[RowBox[List[SubscriptBox["c", "1"], " ", RowBox[List["h", "[", "z", "]"]], " ", RowBox[List["Cos", "[", RowBox[List["g", "[", "z", "]"]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", RowBox[List["h", "[", "z", "]"]], " ", RowBox[List["Sin", "[", RowBox[List["g", "[", "z", "]"]], "]"]]]]]]]]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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