How do we solve a system of coupled differential equations written below?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

-\frac{d^2}{dr^2}\left(

\begin{array}{c}

\phi_{l,bg}(r) \\

\phi_{l,c}(r) \\

\end{array} \right)+ \left(

\begin{array}{cc}

f(r) & \alpha_1 \\

\alpha_2 & g(r)\\

\end{array} \right).\left(

\begin{array}{c}

\phi_{l,bg}(r) \\

\phi_{l,c}(r) \\

\end{array} \right) = E\left(

\begin{array}{c}

\phi_{l,bg}(r) \\

\phi_{l,c}(r) \\

\end{array} \right)

[/tex]

Here [itex]f(r)[/itex] and [itex]g(r)[/itex] are quadratic functions of [itex]r[/itex]. [itex]\alpha_1,\alpha_2\text{ and }E[/itex] are constants.

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# Solving second order coupled differential equation

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