% This file:
%   http://anggtwu.net/LATEX/2023-2-C2-edovs-defs.tex.html
%   http://anggtwu.net/LATEX/2023-2-C2-edovs-defs.tex
%          (find-angg "LATEX/2023-2-C2-edovs-defs.tex")
% Author: Eduardo Ochs <eduardoochs@gmail.com>
%
% (defun e () (interactive) (find-angg "LATEX/2023-2-C2-edovs-defs.tex"))
% (defun o () (interactive) (find-angg "LATEX/2023-2-C2-mv-defs.tex"))

% (c2m232edovsp 6 "defs-e-exemplos")
% (c2m232edovsa   "defs-e-exemplos")
% (c2m231p2p 2 "questao-1")
% (c2m231p2a   "questao-1")


% «.reset»		(to "reset")
% «.DFI»		(to "DFI")

\sa    {[M]}{\CFname{M}{}}
\sa   {[F3]}{\CFname{F}{_3}}
\sa   {[F2]}{\CFname{F}{_2}}
\sa   {[S1]}{\CFname{S}{_1}}
\def\P#1{\left( #1 \right)}


% «reset»  (to ".reset")
\sa{reset}{
  \sa           {G(x)} {G(x)}
  \sa           {H(y)} {H(y)}
  \sa           {g(x)} {g(x)}
  \sa           {h(y)} {h(y)}
  \sa        {Hinv(u)} {H^{-1}(u)}
  \sa     {Hinv(H(y))} {H^{-1}(H(y))}
  \sa {Hinv(G(x)+C_3)} {H^{-1}(G(x)+C_3)}
  }
\ga{reset}

\sa{reset-S1}{
  \sa           {g(x)} {-2x}
  \sa           {h(y)} {2y}
  \sa           {G(x)} {-x^2}
  \sa           {H(y)} {y^2}
  \sa        {Hinv(u)} {\sqrt{u}}
  \sa     {Hinv(H(y))} {\sqrt{y^2}}
  \sa {Hinv(G(x)+C_3)} {\sqrt{-x^2+C_3}}
  }


% Based on:
% (c2m231p2p 2 "questao-1")
% (c2m231p2a   "questao-1")
\sa{(M)}{
  \left(\begin{array}{rcl}
             \D \dydx &=& \D \frac{\ga{g(x)}}{\ga{h(y)}} \\
        \ga{h(y)}\,dy &=& \ga{g(x)}\,dx       \\ \\[-10pt]
     \inty{\ga{h(y)}} &=& \intx{\ga{g(x)}}    \\
           \mcc{\veq} & & \mcc{\veq}          \\
  \mcc{\ga{H(y)}+C_1} & & \mcc{\ga{G(x)}+C_2} \\ \\[-10pt]
        \ga{H(y)}     &=& \ga{G(x)}+C_2-C_1   \\
                      &=& \ga{G(x)}+C_3       \\ \\[-10pt]
      \ga{Hinv(H(y))} &=& \ga{Hinv(G(x)+C_3)} \\
           \mcc{\veq} & & \\
              \mcc{y} & & \\
   \end{array}
   \right)
  }
\sa{(F3)}{
  \left(\begin{array}{rcl}
             \D \dydx &=& \D \frac{\ga{g(x)}}{\ga{h(y)}} \\ \\[-10pt]
      \ga{Hinv(H(y))} &=& \ga{Hinv(G(x)+C_3)} \\
           \mcc{\veq} & & \\
              \mcc{y} & & \\
   \end{array}
   \right)
  }
\sa{(F2)}{
  \left(\begin{array}{rcl}
             \D \dydx &=& \D \frac{\ga{g(x)}}{\ga{h(y)}} \\ \\[-10pt]
                    y &=& \ga{Hinv(G(x)+C_3)} \\
   \end{array}
   \right)
  }
\sa{(S)}{
  \left[\begin{array}{rcl}
             g(x) &:=& \ga{g(x)} \\
             h(y) &:=& \ga{h(y)} \\
             G(x) &:=& \ga{G(x)} \\
             H(y) &:=& \ga{H(y)} \\
        H^{-1}(u) &:=& \ga{Hinv(u)} \\
   \end{array}
   \right]
  }




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