SetDirectory[$HomeDirectory<>"/Documents/handouts/math467/Sturm-Liouville"]

Example 01

gf=GreenFunction[{u''[x]+16u[x],u[0]==0,u'[1]==0},u[x],{x,0,1},y]

Integrate[(((y+1))^2)gf,{y,0,1}]

u[x_]:=((((x+1))^2)-1/8)/16-7Cos[4x-4]/(128Cos[4])-Sin[4x]/(16Cos[4])

Plot3D[gf,{x,0,1},{y,0,1},AxesLabel->{"\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["x", "TI"], TraditionalForm], "errors" -> {}, "input" -> "x", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)","\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["y", "TI"], TraditionalForm], "errors" -> {}, "input" -> "y", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)","\!\(\*TemplateBox[<|"boxes" -> FormBox[
RowBox[{
StyleBox["G", "TI"], "(", 
RowBox[{
StyleBox["x", "TI"], ";", 
StyleBox["y", "TI"]}], ")"}], TraditionalForm], "errors" -> {}, "input" -> "G (x; y)", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)"},BaseStyle->FontSize->12]

Export["example03.pdf",%,"PDF"]

Export["example03.eps",%%,"EPS"]