- #1
blenx
- 30
- 0
Here is the equation I don't know how to solve:
<br /> \begin{aligned}<br /> \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _1^2} \right){u_1} = {g_1}u_2^{}{u_3} \\ <br /> \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _2^2} \right){u_2} = {g_2}u_1^{}{u_3} \\ <br /> \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _3^2} \right){u_3} = {g_3}u_2^{}{u_1} \\ <br /> \end{aligned}<br />
where {\beta _i},{g_i} are constants.
Is there an exact solution to this problem? If not, how to solve it approximately or numerically?
<br /> \begin{aligned}<br /> \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _1^2} \right){u_1} = {g_1}u_2^{}{u_3} \\ <br /> \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _2^2} \right){u_2} = {g_2}u_1^{}{u_3} \\ <br /> \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _3^2} \right){u_3} = {g_3}u_2^{}{u_1} \\ <br /> \end{aligned}<br />
where {\beta _i},{g_i} are constants.
Is there an exact solution to this problem? If not, how to solve it approximately or numerically?
