The ordinary differential equations to solve have symbolic parameters $k_1,k_2,k_3,k_4,k_5,k_6 \in \mathbb{R}$. $$ \left\{ \begin{array}{l} {y_1}'(t)=-{k_1} {y_1}(t)-{k_2} {y_1}(t),\\ {y_2}'(t)={k_2} {y_1}(t)-{k_3} {y_2}(t),\\ {y_3}'(t)={k_1} {y_1}(t)+{k_3} {y_2}(t)-{k_4} {y_3}(t),\\ {y_4}'(t)={k_4} {y_3}(t)-{k_5} {y_2}(t) {y_4}(t)+{k_6} {y_5}(t),\\ {y_5}'(t)={k_5} {y_2}(t) {y_4}(t)-{k_6} {y_5}(t)\\ \end{array} \right.$$
The ODE system itself seems simple when all $k_i$ are numerical numbers. How to solve it symbolically ? Is it possible to obtain explicit solutions?
Update:
Expressions in MMA:(DSolve does not work for such nonlinear ODE system)
DSolve[{D[y1[t], t] == -k1*y1[t] - k2*y1[t],
D[y2[t], t] == k2*y1[t] - k3*y2[t],
D[y3[t], t] == k1*y1[t] + k3*y2[t] - k4*y3[t],
D[y4[t], t] == k4*y3[t] - k5*y2[t]*y4[t] + k6*y5[t],
D[y5[t], t] == k5*y2[t]*y4[t] - k6*y5[t]}, {y1[t], y2[t], y3[t],
y4[t], y5[t]}, t]