I have the following system of ODEs. Can anybody please suggest how can I solve this system? I have tried Maple but it not giving any output, it just gets hang. \begin{align} -(c+\alpha)f^{\prime}+(a_{1}-a_{2}c)g^{\prime\prime}+(bg+\sigma f^{\prime})(f^{2}+g^{2})-2(\lambda+\mu)f(ff^{\prime}+gg^{\prime})-\lambda f^{\prime}(f^{2}+g^{2})=\,0,\\ (c+\alpha)g^{\prime}+(a_{1}-a_{2}c)f^{\prime\prime}+(bf-\sigma g^{\prime})(f^{2}+g^{2})+2g(\lambda+\mu)(ff^{\prime}+gg^{\prime})+\lambda g^{\prime}(f^{2}+g^{2})=\,0 \end{align}
Here $'=\frac{d}{dt}$, where $c, \alpha, b, \lambda, \mu$ are all constants.