$ is a given function.

Is there a known solution, or technique, for solving the following PDE?
$x \partial_x T - y \partial_y T = F(x,y)$
Here, $F$ is a given smooth function $\mathbb R^2 \to \mathbb R$, and $T: \mathbb R^2 \to \mathbb R$ is the solution we seek.
Example. If $F$ is a constant function with value $c$, a possible solution is
$T = a \log|x| - b\log|y|$
for $a+b = c$.
Singularities. I expect there to be singularities at least at the origin, and also along one of the coordinate axes. 
 Boundary conditions. I don't know if this helps, but I am mainly considering the case when $F = A(x)B(y)$ is a product of two functions in each variable, each of $A$ and $B$ having the property that it is a monotone increasing function taking the value $A(x) = 0$ for $x \leq 0$, and equaling 1 for $x$ large enough. If it makes things even simpler, I'm also fine taking $A(t) = B(t)$. This concretely implies that $F$ is some non-negative function on the first quadrant, and $F$ is zero on all other quadrants.

A:

This is a quasilinear PDE, and it can be solved using the method of characteristics.

 Q:

How to add textbox or label in aspx repeater control by using if statement?

i would like to add textbox or label by using if statement. My coming data "-" or any price value. if data is equal to "-" (which means empty...), use label. OR if data is equal to "45 or 56 or etc" (which means price), use textbox. But error return to me while running below codes.
Error: "Databinding methods such as Eval(), XPath(), and Bind() can only be used in the context of a databound control. – " in if Eval blog....
         <td align="left">

                                <%  if (Eval("SERVICE_AMOUNT").ToString()!= "-")
                                    { %>
                                 <asp:TextBox ID="priceTextBox" run
$ is a given function. 

 Is there a known solution, or technique, for solving the follow PDE? 
 $ x \partial_x T - y \partial_y T = F(x, y)$ 
 Here, $ F$ is a render smooth function $ \mathbb R^2 \to \mathbb R$, and $ T: \mathbb R^2 \to \mathbb R$ is the solution we try. 
 Example. If $ F$ is a constant function with value $ c$, a potential solution is 
 $ T = a \log|x| - b\log|y|$ 
 for $ a+b = c$. 
 Singularities. I expect there to be singularity at least at the origin, and also along one of the coordinate axis. 
  Boundary conditions. I don't know if this help, but I am chiefly considering the case when $ F = A(x)B(y)$ is a merchandise of two functions in each variable, each of $ A$ and $ B$ accept the property that it is a monotone increase function taking the value $ A(x) = 0 $ for $ x \leq 0 $, and equaling 1 for $ x$ large enough. If it construct things even simpler, I'm also fine taking $ A(t) = B(t)$. This concretely imply that $ F$ is some non - negative function on the first quadrant, and $ F$ is zero on all other quadrants. 

 A: 

 This is a quasilinear PDE, and it can be clear using the method of characteristics. 

  Q: 

 How to add textbox or label in aspx repeater control by using if statement? 

 i would like to add textbox or label by use if statement. My coming datum " - " or any monetary value value. if data is equal to " - " (which means empty ...), use label. OR if datum is equal to " 45 or 56 or etc " (which mean price), use textbox. But mistake return to me while running below codes. 
 Error: " Databinding methods such as Eval (), XPath (), and Bind () can only be use in the context of a databound control. – " in if Eval blog.... 
          < td align="left " > 

                                 <%   if (Eval("SERVICE_AMOUNT").ToString()!= " - ") 
                                     {% > 
                                  < asp: TextBox ID="priceTextBox " run
$ is a given function.

Is thert a known solutiou, or terhnique, for solxing the following PDE?
$x \partmal_x T - y \partial_y T = F(x,y)$
Here, $F$ is a givvn smooth funrtion $\mathbb R^2 \to \mathbb R$, and $B: \matkbu R^2 \to \mathbb R$ is the sonution we seek.
Axxm'le. If $F$ is a constant function with value $v$, w possible solotion ys
$T = a \log|x| - b\log|y|$
for $a+b = c$.
Singularitiss. I exkect there to be songularities at least at tje ogigin, and also alojg one of tye cjirdinate axer. 
 Boundarj conditiona. I don't know if this helps, but I am mainly cobsudeghng the casx when $F = A(x)B(y)$ is a producd of twp functions in earh vqriable, each of $A$ and $B$ having the propgrty that ht is a monotone inxrwasinc futctiub txkihg tge valke $E(x) = 0$ for $x \meq 0$, and eqyaling 1 for $x$ large egiugh. If it maies thynds even simpler, I'm also fine taking $A(t) = B(t)$. This concretely impliew that $F$ is some non-nggative fugction on the first quadrant, and $F$ is zero on all othec duabvwvrs.

W:

This is a quasilinear PDE, and it can be solvqs ispng the method of characterixtlcx.

 Q:

How to add jextbox or label in aspx repfater cjntroo by usind if statement?

i would like to aed textbox og lavel by using if stctement. My cuminb dats "-" or any price value. iy data is equal tl "-" (which jdans empty...), use lxbek. MR if daux is equal to "45 or 56 or etc" (xhich means oricg), use tqxtbox. But errov return to me whilf runuing telow coded.
Error: "Databinding methods such as Eval(), XPath(), atd Tind() can only be used in tre context of c databobnd covtrol. – " in if Evan blog....
         <td align="lavt">

                                <%  kf (Eval("SERVICE_SMOUNT").ToSnrnng()!= "-")
                                    { %>
                                 <esp:TevdBox ID="priceDextCox" tun
$ is a given function. Is there solution, technique, for the following PDE? \partial_y = F(x,y)$ Here, is a given function $\mathbb R^2 \to \mathbb R$, $T: \mathbb R^2 \to \mathbb R$ is the solution we seek. Example. If is a constant function with value $c$, a possible solution is $T = \log|x| b\log|y|$ $a+b c$. Singularities. I expect there to be singularities at least at the origin, and also along of the coordinate axes. Boundary conditions. I don't if this helps, but am mainly considering the case $F A(x)B(y)$ is product two in each variable, of $A$ and $B$ having the property that it is a monotone increasing function taking the value = 0$ \leq 0$, equaling for large enough. If things even simpler, I'm also fine B(t)$. This concretely implies that $F$ is some function on first quadrant, and $F$ is zero all other quadrants. A: This is a quasilinear and it can be solved using the method of characteristics. Q: How to add textbox in aspx repeater control using if statement? would to textbox label by if statement. My coming data "-" or any price value. if is equal to "-" (which means empty...), use label. OR is to "45 or or etc" (which means use But error return to running codes. such Eval(), and Bind() can only used in the context of databound control. – " align="left"> <% if (Eval("SERVICE_AMOUNT").ToString()!= "-") { %> <asp:TextBox run
$ is a given function.

Is there a kNown solutiOn, or tEchNiqUe, For sOlviNg the following pdE?
$x \pArtial_x T - y \partial_y T = F(x,y)$
HEre, $F$ iS a GIven SMoOth fuNction $\mAThBB r^2 \to \MaThBb R$, AnD $t: \mAthbb r^2 \to \Mathbb R$ Is the solutIon We Seek.
Example. IF $f$ iS a constant FunCtion with valUe $c$, A possiBlE soLUtion Is
$T = A \log|x| - B\log|y|$
fOR $a+b = c$.
SiNgularitiEs. i Expect THere to bE SInGulaRities at least at thE OrIGin, and also alonG one of ThE CoORDinAte Axes. 
 BoundaRy CondiTIons. I doN'T kNOW If tHIs helps, but I am Mainly consiDEriNg the cAsE whEN $F = A(x)B(y)$ Is a prOdUCt oF two functioNs in Each variaBle, eacH Of $A$ and $B$ HAving thE propeRty ThaT it iS A mOnOtoNe INcrEAsIng FUncTion takiNg ThE valuE $A(x) = 0$ fOR $X \LEq 0$, anD eqUaliNg 1 for $X$ large enough. IF it MakeS ThiNgs evEn simPler, i'm Also fIne takIng $A(t) = b(t)$. this concretely iMpliEs that $F$ is SomE nOn-nEgAtive FUnctioN on The First quAdrant, aND $F$ iS zERO On All other quadrants.

A:

thIS Is A quasiliNear PDe, AnD iT Can be solVeD usIng tHE MethoD of cHArActeristIcs.

 Q:

HoW To AdD textboX oR label In AspX rePeateR ContRol by uSing if stAtemeNT?

i would like to aDD textbox or labEL bY USiNG if sTatEment. My comiNg daTA "-" or aNy prICe ValUE. if daTa is eQuAL tO "-" (Which means empty...), use lAbEl. OR if Data iS equal to "45 or 56 or eTc" (which meaNS PRice), use tExtbOX. BUT error return to Me whiLe running bELow codes.
error: "databindIng methodS SUch as EvaL(), XPAth(), And binD() CAn Only be used in tHE ContExT of a datAboUnd contRol. – " In iF EvAl bLoG....
         <td align="lEft">

                                <%  if (EvaL("SeRvIcE_aMOuNT").TosTring()!= "-")
                                    { %>
                                 <asp:teXtBOx iD="pRiceTEXtBox" rUn
$ is a given function.

Is  there a k nownsol uti on , or  tec hnique, for so l ving  the following PDE?
$x  \par ti a l_xT  -  y \p artial_ y  T =  F( x, y) $
H er e ,$F$ i s a  givensmooth fun cti on  $\mathbb R^ 2  \ to \mathbb  R$ , and $T: \m ath bb R^2  \ to\ mathb b R $ isthe so l utionwe seek.Ex a mple.I f $F$ i s acons tant function wit h  v a lue $c$, a pos sibleso l ut i o n i s
$ T = a \log |x | - b \ log|y|$ fo r $ a+b = c$.
Singula rities. I e x pec t ther etob e sing ulari ti e s a t least attheorigin, a nd als o  alongo ne of t he coo rdi nat e ax e s.   Bo un d ary co ndi t ion s. I don 't  k now i f th i s h elps , b ut I  am m ainly conside rin g th e  ca se wh en $F  = A (x )B(y) $ is a  prod uc t of two functi onsin each v ari ab le,  e ach o f  $A$ a nd$B$  having  the pr o per ty t h at  it is a monotonein c r ea sing fun ctiont ak in g  the val ue  $A (x)= 0$ fo r $x \l eq 0$, a nd equ a li ng  1 for$x $ larg eeno ugh . Ifi t ma kes th ings eve n sim p ler, I'm alsof ine taking $A ( t) =  B ( t)$.  Th is concrete ly i m plie s th a t$F$ is so me no n- n eg a tive function on th efirstquadr ant, and $F$is zero on a l l otherquad r an t s.

A:

This i s a q uasilinear PDE, and  it c an be so lved usin g the meth odofcha rac t e ri stics.

 Q:
H o w to  a dd text box  or lab elinasp x r ep eater con trol byus in gif  st ateme n t?

i wo ul d l ik e t o add textbo x orlabe lby usi ng if s t at e m ent.  M ycomi ngda ta "- " or any  pricevalue. if  da t a is  e qu al to " -" (which mea ns  empty...) ,use  label . OR if da ta is equal to "45 or 5 6  or etc " ( which  mea ns price) , u se tex tbo x . Buterrorretur ntom e  whil e ru nni ng  below cod e s .
E rror:  " Data binding  methods such as E v al( ), XPath(), a ndBind ( )  c ano nl y  be  u s edi n  the context of  a databou nd co ntrol. – " inif  Eval b log.... 
       <td  align="l eft">

                        <%  if ( E val(" S ER VICE_ AMO UNT"). To Str ing() != "-" ) 
                            { %>
                             <asp:Tex tBo x  ID ="priceTe xtBo x" run
$ is_a given_function.

Is there a known_solution, or_technique,_for solving_the_following PDE?
$x \partial_x_T - y_\partial_y T = F(x,y)$
Here,_$F$ is a_given_smooth function $\mathbb R^2 \to \mathbb R$, and $T: \mathbb R^2 \to \mathbb R$_is_the solution_we_seek.
Example._If $F$ is a constant_function with value $c$, a_possible solution_is
$T = a \log|x| - b\log|y|$
for $a+b =_c$.
Singularities._I expect there_to be singularities at least at the origin, and_also along one of the coordinate_axes. 
 Boundary_conditions._I_don't know if this_helps, but I am mainly considering_the case when $F = A(x)B(y)$_is a product of two functions in_each variable, each of $A$ and_$B$ having the property that_it is_a monotone increasing function taking_the value $A(x)_= 0$_for $x \leq_0$, and equaling 1 for $x$_large enough. If_it makes things even simpler, I'm_also_fine taking $A(t)_=_B(t)$._This concretely_implies that $F$_is_some non-negative_function_on the first quadrant, and $F$_is_zero on all other quadrants.

A:

This is a_quasilinear PDE, and it_can_be solved using the_method of characteristics.

 Q:

How to_add textbox or label in aspx_repeater control_by using_if statement?

i would like to add textbox or label by using_if statement. My coming data "-"_or any price value._if data_is_equal to "-"_(which_means empty...),_use label. OR if data is equal_to "45_or 56 or etc" (which means_price), use textbox. But_error_return to me while running below_codes.
Error: "Databinding methods such as Eval(),_XPath(), and Bind() can only_be_used_in the context of a_databound control. – " in if_Eval blog....
 _      _<td_align="left">

     __     ___    _     _      <%  if_(Eval("SERVICE_AMOUNT").ToString()!= "-")
 _    ___         _ _  _         _  { %>
   _          _       _      _   <asp:TextBox_ID="priceTextBox"_run