I have an equation system where the right hand side contains a time 
derivative, looking like

<https://lh3.googleusercontent.com/-zRtosh4pbeY/WW4KxK2_2qI/AAAAAAAACPQ/Ln8NbS9GxMQ5JUYTQIbuj7g19BvGh9mnwCLcBGAs/s1600/time_derivative.png>

Without that time derivative I can solve it, but I do not know how to 
include it here. Are there possible guidelines for that? One idea I got is 
from here 
<https://scicomp.stackexchange.com/questions/27363/approach-for-coupled-equations-with-included-time-derivative>,
 
but this can not applied to the code in my case (used example 52 as 
starting point), as I assume.

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