Implicit solution of ODE to explicit or approximate explicit function Working with the following ODE and implicit solution but need an explicit solution for J:
The ODE with$J_c$ and $G$ as constants is: 
$$-\frac{1}{J^2}\frac{dJ}{dt} = G(J-J_c)$$
The implicit solution given by Field et al. (1995) is:
$$Gt = \frac{1}{J_c^2} \left[ ln \left( \frac{J}{J_o}\cdot \frac{J_o-J_c}{J-J_c}   \right) - J_c \left(\frac{1}{J}- \frac{1}{J_o} \right) \right] $$
There is no explicit statement about $J_o$ in the reference but physically it corresponds to the initial flux at time zero. This suggests that $J=J_o \text{ at time}~ t=0$. However as suggested and shown by JJacquelin when we plug in for $t=0$ we get $ln(1) = 0$ ? Checking the -ve sign in the original reference as suggested by JJacquelin. 
Any pointers to a complete explicit solution or good approximate of an explicit solution is greatly appreciated.
Thanks,
Vince

Based on contribution from JJacquelin the problem needs a numerical approach to solve. No solution based on standard functions (possibly non-standard) is likely.
