You can refer to the paper

Artificial neural networks for solving ordinary and partial differential equations

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=712178&newsearch=true&queryText=Artificial%20Neural%20Networks%20for%20Solving%20Ordinary%20and%20Partial%20Differential%20Equations

I read some such papers. But I wanted reply for some people who is actually working on this area. So that I can get a concrete answer.

Also that paper is of 1998, so I was interested if there is any recent trend in researchers to solve differential equation using artificial neural network and is that actually viable in some way?

You can check the work of Prof. Chakraverty (for example http://www.academia.edu/1896867/Artificial_Neural_Network_Based_Numerical_Solution_of_Ordinary_Differential_Equations)