How can I verifying in a simple way that the following system of differential (and algebric) equations has not solution? The unknown quantities are $Q_d,C_d,C_a,C_i$ and the boundary conditions are $Q_d(0)=0$ and so on. The quantities $Q_a,k_a,k_d,k_o$ are positive constants.
$$\frac{d\left( Q_d C_d \right) }{dx} = k_d \left( C_i - C_d \right)$$
$$\frac{dQ_d }{dx} = k_o \left( C_d - C_i \right)$$
$$Q_a \frac{dC_a }{dx} = k_a (C_a-C_i)$$
$$k_a (C_a-C_i) = k_d \left( C_i - C_d \right)$$
Thank you so much for your time.