- #1

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## Main Question or Discussion Point

[tex]

\left[\begin{array}{c}

y'_1(x) \\ \vdots \\ y'_n(x) \\

\end{array}\right]

=

\left[\begin{array}{ccc}

f_{11}(y) & \cdots & f_{1n}(y) \\

\vdots & & \vdots \\

f_{n1}(y) & \cdots & f_{nn}(y) \\

\end{array}\right]

\left[\begin{array}{c}

g_1(x) \\ \vdots \\ g_n(x) \\

\end{array}\right]

[/tex]

If n=1, then this can be solved with the separation technique. Suppose n>1 and that [itex]f[/itex] is invertible. Could the separation technique be generalized to give some explicit formula for solution y(x)? I tried without success. Anyone dealt with problems like this ever?

\left[\begin{array}{c}

y'_1(x) \\ \vdots \\ y'_n(x) \\

\end{array}\right]

=

\left[\begin{array}{ccc}

f_{11}(y) & \cdots & f_{1n}(y) \\

\vdots & & \vdots \\

f_{n1}(y) & \cdots & f_{nn}(y) \\

\end{array}\right]

\left[\begin{array}{c}

g_1(x) \\ \vdots \\ g_n(x) \\

\end{array}\right]

[/tex]

If n=1, then this can be solved with the separation technique. Suppose n>1 and that [itex]f[/itex] is invertible. Could the separation technique be generalized to give some explicit formula for solution y(x)? I tried without success. Anyone dealt with problems like this ever?