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Can you give some suggestions to solve the following system of 1st order nonlinear differential equations?

Thank you.

[tex]

\[

\begin{array}{l}

u'(t) = Au^2 (t) + B(t)u + C(t) \\

u(t) = \left[ {\begin{array}{*{20}c}

{x_1 (t)} \\

{x_2 (t)} \\

\end{array}} \right] \\

A = \left[ {\begin{array}{*{20}c}

{a_{11} } & {a_{12} } \\

{a_{21} } & {a_{22} } \\

\end{array}} \right] \\

B(t) = \left[ {\begin{array}{*{20}c}

{f_{11} (t)} & {f_{12} (t)} \\

{f_{21} (t)} & {f_{22} (t)} \\

\end{array}} \right] \\

C(t) = \left[ {\begin{array}{*{20}c}

{g_{11} (t)} & {g_{12} (t)} \\

{g_{21} (t)} & {g_{22} (t)} \\

\end{array}} \right] \\

\end{array}

\]

[/tex]

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# A system of 1st order nonlinear differential equations

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