How do I write the form of the solution to this equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\dot{\vec{x}}(t) =

\left [ \begin{array}{cc}

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

a_{21}(t) & a_{22}(t)

\end{array} \right ] \vec{x}(t)

[/tex]

I just need to be able to write x_{1}(t) and x_{2}(t) so I can do the rest of the problem I'm working on. Getting this would just be a small step in my solution, but I am very rusty with my differential equations!! :(

Initially, I thought to write:

[tex]

x_1(t) = \int_{t_0}^{t}x_1(\tau)a_{11}(\tau) + x_2(\tau)a_{12}(\tau)d\tau

[/tex]

[tex]

x_2(t) = \int_{t_0}^{t}x_1(\tau)a_{21}(\tau) + x_2(\tau)a_{22}(\tau)d\tau

[/tex]

But that has the solutions with dependence on x_{1}(t) and x_{2}(t). That's not the way to write it, is it?

Thanks.

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# Homework Help: Solution to Matrix Differential Equation

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