Please suggest me different CAD tools available for MEMS that will allow me to integrate other devices with MEMS (device description is based on differential equations) to study the system behaviour as a whole.
COMSOL Multiphysics is one software that involves equation based modeling. You can check those links if could help: https://goo.gl/YGJDN1 .
Also, a better and more time convenient method is to develop a Verilog-A model that characterize your whole system. Given that you already have one device described in differential equations you can model the other device also and write a complete model for the system and thus you can simulate them easily using any circuit simulation tools (e.g., Cadence Virtuoso).