# A general relativity question about the Einstein equations?

Assuming a Robertson-Walker metric to describe homogeneous and isotropic cosmological models, Einstein equations with cosmological constant reduce to these 3 non-linear ordinary differential equations for a perfect fluid:

\begin{align} \dot{\rho} &= -3H(\rho + P) \tag{1} \\ \dot{H} &= -H^2-4\pi G(\rho + 3P)/3 + \lambda/3 \tag{2} \\ H^2 &= 8\pi G\rho/3-K/a^2+\lambda/3 \tag{3} \end{align}

Here, dot represent the derivative with respect to time and the function $H=H(t)= \dot{a}/a$ where $a = a(t)$ is the scale factor.

I know that (1) is the conservation of energy equation but i can't understand what (2) and (3) represent?

You can arrive at equations (2) and (3) by plugging the Robertson-Walker metric into the Einstein field equations. The universe is modelled as a perfect fluid so the energy-momentum tensor is $(T_{ab})=\text{Diag}(\rho,P,P,P)$ and the first equation comes from the $T_{00}$ (time) part of the field equations, the second from the spacial part once you have plugged in the metric.
Note that the three equations are not independent, though any choice of two of them are, the continuity equation (1) $\nabla^a T_ab =0$ may be obtained directly from the field equations by applying $\nabla^a$ and applying the Bianchi identity and metricity property of the Levi-Civita connection.