- #1
quacam09
- 16
- 0
Hello,
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]
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]