$s_1^{'}(t) = -(\mu + \lambda) s_1(t) + \mu s_1^{2}(t) + \lambda s_{0}(t) $
with initial conditions $s_1(0) = 1$. $\lambda$ and $\mu$ are constant, and $s_{0}(t) = \frac{\mu + \lambda}{\mu + \lambda e^{(\mu+\lambda)t}}$
The differential equation is second order with variable coefficients.
Anyone can help me? I am stuch in the finding the solution of this differential equation.